D100 · locale=en · zero-copy common adapter

Algebraic Geometry: Curves, Sheaves and Schemes

A verified identity-and-route projection over the complete 30-unit classical volume, complete 30-unit BGK volume, and separate 32-unit editorial companion. The central id-ID course truth is not rewritten.

60 source-course units32 companion units1,201 exercises160 complete exercise solutions1,041 explicit negative states

Educator evidence view · English release assets · Native English reader hub

D100:AK:01

Algebraic Curves · Unit 1: Lecture 1: Plane Algebraic Curves

51 native section identities · 28 exercises · 7 complete solutions

28 exercises
  1. Exercise 1.1 · no public source solution
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  4. Exercise 1.4 · complete solution
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D100:AK:02

Algebraic Curves · Unit 2: Lecture 2: Affine Algebraic Sets

54 native section identities · 27 exercises · 9 complete solutions

27 exercises
  1. Exercise 2.1 · no public source solution
  2. Exercise 2.2 · complete solution
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D100:AK:03

Algebraic Curves · Unit 3: Lecture 3: The Zariski Topology, Vanishing Ideals, and Radicals

53 native section identities · 22 exercises · 2 complete solutions

22 exercises
  1. Exercise 3.1 · no public source solution
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D100:AK:04

Algebraic Curves · Unit 4: Lecture 4: Irreducibility, Components, and Intersections of Curves

55 native section identities · 30 exercises · 6 complete solutions

30 exercises
  1. Exercise 4.1 · no public source solution
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D100:AK:05

Algebraic Curves · Unit 5: Lecture 5: Homogeneous Components, Noether Normalisation, and Polynomial Maps

53 native section identities · 27 exercises · 4 complete solutions

27 exercises
  1. Exercise 5.1 · no public source solution
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  3. Exercise 5.3 · complete solution
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D100:AK:06

Algebraic Curves · Unit 6: Lecture 6: Polynomial and Rational Parametrisations

60 native section identities · 30 exercises · 9 complete solutions

30 exercises
  1. Exercise 6.1 · no public source solution
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  3. Exercise 6.3 · complete solution
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D100:AK:07

Algebraic Curves · Unit 7: Lecture 7: Conic Sections and Quadrics

53 native section identities · 33 exercises · 3 complete solutions

33 exercises
  1. Exercise 7.1 · no public source solution
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D100:AK:08

Algebraic Curves · Unit 8: Lecture 8: Mechanically Defined Algebraic Curves

42 native section identities · 24 exercises · 2 complete solutions

24 exercises
  1. Exercise 8.1 · no public source solution
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D100:AK:09

Algebraic Curves · Unit 9: Lecture 9: Noetherian Rings, Hilbert's Basis Theorem, and Modules

61 native section identities · 24 exercises · 3 complete solutions

24 exercises
  1. Exercise 9.1 · no public source solution
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D100:AK:10

Algebraic Curves · Unit 10: Lecture 10: Noetherian modules and Hilbert's Nullstellensatz

60 native section identities · 29 exercises · 6 complete solutions

29 exercises
  1. Exercise 10.1 · complete solution
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D100:AK:11

Algebraic Curves · Unit 11: Lecture 11: Hilbert's Nullstellensatz and coordinate rings

59 native section identities · 26 exercises · 2 complete solutions

26 exercises
  1. Exercise 11.1 · no public source solution
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D100:AK:12

Algebraic Curves · Unit 12: Lecture 12: The $K$-spectrum and its functoriality

56 native section identities · 30 exercises · 2 complete solutions

30 exercises
  1. Exercise 12.1 · no public source solution
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D100:AK:13

Algebraic Curves · Unit 13: Lecture 13: The open sets $D(f)$, connectedness, and idempotent elements

74 native section identities · 37 exercises · 14 complete solutions

37 exercises
  1. Exercise 13.1 · no public source solution
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  3. Exercise 13.3 · complete solution
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D100:AK:14

Algebraic Curves · Unit 14: Lecture 14: Algebraic Functions on Varieties

54 native section identities · 27 exercises · 2 complete solutions

27 exercises
  1. Exercise 14.1 · no public source solution
  2. Exercise 14.2 · complete solution
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D100:AK:15

Algebraic Curves · Unit 15: Lecture 15: Affine and Quasi-affine Varieties, Local Rings, and Stalks

60 native section identities · 29 exercises · 4 complete solutions

29 exercises
  1. Exercise 15.1 · no public source solution
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D100:AK:16

Algebraic Curves · Unit 16: Lecture 16: Irreducible Filters, Morphisms, and Fibres

53 native section identities · 23 exercises · 6 complete solutions

23 exercises
  1. Exercise 16.1 · complete solution
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D100:AK:17

Algebraic Curves · Unit 17: Lecture 17: Monoid Rings and Groups of Differences

71 native section identities · 39 exercises · 4 complete solutions

39 exercises
  1. Exercise 17.1 · no public source solution
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  3. Exercise 17.3 · complete solution
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D100:AK:18

Algebraic Curves · Unit 18: Lecture 18: Monomial Curves and Numerical Monoids

58 native section identities · 28 exercises · 5 complete solutions

28 exercises
  1. Exercise 18.1 · no public source solution
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  3. Exercise 18.3 · complete solution
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D100:AK:19

Algebraic Curves · Unit 19: Lecture 19: Quotient Ring Presentations and Integrality

39 native section identities · 15 exercises · 2 complete solutions

15 exercises
  1. Exercise 19.1 · no public source solution
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  4. Exercise 19.4 · complete solution
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  8. Exercise 19.8 · no public source solution
  9. Exercise 19.9 · no public source solution
  10. Exercise 19.10 · no public source solution
  11. Exercise 19.11 · no public source solution
  12. Exercise 19.12 · complete solution
  13. Exercise 19.13 · no public source solution
  14. Exercise 19.14 · no public source solution
  15. Exercise 19.15 · no public source solution

D100:AK:20

Algebraic Curves · Unit 20: Lecture 20: Normal Rings and Normalisation

58 native section identities · 23 exercises · 8 complete solutions

23 exercises
  1. Exercise 20.1 · complete solution
  2. Exercise 20.2 · no public source solution
  3. Exercise 20.3 · complete solution
  4. Exercise 20.4 · complete solution
  5. Exercise 20.5 · complete solution
  6. Exercise 20.6 · no public source solution
  7. Exercise 20.7 · no public source solution
  8. Exercise 20.8 · no public source solution
  9. Exercise 20.9 · no public source solution
  10. Exercise 20.10 · no public source solution
  11. Exercise 20.11 · no public source solution
  12. Exercise 20.12 · complete solution
  13. Exercise 20.13 · complete solution
  14. Exercise 20.14 · complete solution
  15. Exercise 20.15 · no public source solution
  16. Exercise 20.16 · no public source solution
  17. Exercise 20.17 · complete solution
  18. Exercise 20.18 · no public source solution
  19. Exercise 20.19 · no public source solution
  20. Exercise 20.20 · no public source solution
  21. Exercise 20.21 · no public source solution
  22. Exercise 20.22 · no public source solution
  23. Exercise 20.23 · no public source solution

D100:AK:21

Algebraic Curves · Unit 21: Lecture 21: Discrete Valuation Rings and Nakayama's Lemma

48 native section identities · 26 exercises · 2 complete solutions

26 exercises
  1. Exercise 21.1 · no public source solution
  2. Exercise 21.2 · no public source solution
  3. Exercise 21.3 · complete solution
  4. Exercise 21.4 · no public source solution
  5. Exercise 21.5 · no public source solution
  6. Exercise 21.6 · no public source solution
  7. Exercise 21.7 · no public source solution
  8. Exercise 21.8 · complete solution
  9. Exercise 21.9 · no public source solution
  10. Exercise 21.10 · no public source solution
  11. Exercise 21.11 · no public source solution
  12. Exercise 21.12 · no public source solution
  13. Exercise 21.13 · no public source solution
  14. Exercise 21.14 · no public source solution
  15. Exercise 21.15 · no public source solution
  16. Exercise 21.16 · no public source solution
  17. Exercise 21.17 · no public source solution
  18. Exercise 21.18 · no public source solution
  19. Exercise 21.19 · no public source solution
  20. Exercise 21.20 · no public source solution
  21. Exercise 21.21 · no public source solution
  22. Exercise 21.22 · no public source solution
  23. Exercise 21.23 · no public source solution
  24. Exercise 21.24 · no public source solution
  25. Exercise 21.25 · no public source solution
  26. Exercise 21.26 · no public source solution

D100:AK:22

Algebraic Curves · Unit 22: Lecture 22: Embedding Dimension and Smooth and Singular Points

57 native section identities · 23 exercises · 9 complete solutions

23 exercises
  1. Exercise 22.1 · no public source solution
  2. Exercise 22.2 · no public source solution
  3. Exercise 22.3 · no public source solution
  4. Exercise 22.4 · no public source solution
  5. Exercise 22.5 · complete solution
  6. Exercise 22.6 · complete solution
  7. Exercise 22.7 · no public source solution
  8. Exercise 22.8 · no public source solution
  9. Exercise 22.9 · complete solution
  10. Exercise 22.10 · complete solution
  11. Exercise 22.11 · no public source solution
  12. Exercise 22.12 · complete solution
  13. Exercise 22.13 · no public source solution
  14. Exercise 22.14 · complete solution
  15. Exercise 22.15 · complete solution
  16. Exercise 22.16 · complete solution
  17. Exercise 22.17 · no public source solution
  18. Exercise 22.18 · complete solution
  19. Exercise 22.19 · no public source solution
  20. Exercise 22.20 · no public source solution
  21. Exercise 22.21 · no public source solution
  22. Exercise 22.22 · no public source solution
  23. Exercise 22.23 · no public source solution

D100:AK:23

Algebraic Curves · Unit 23: Lecture 23: Cotangent Spaces and Hilbert–Samuel Multiplicity

41 native section identities · 12 exercises · 2 complete solutions

12 exercises
  1. Exercise 23.1 · no public source solution
  2. Exercise 23.2 · no public source solution
  3. Exercise 23.3 · no public source solution
  4. Exercise 23.4 · complete solution
  5. Exercise 23.5 · complete solution
  6. Exercise 23.6 · no public source solution
  7. Exercise 23.7 · no public source solution
  8. Exercise 23.8 · no public source solution
  9. Exercise 23.9 · no public source solution
  10. Exercise 23.10 · no public source solution
  11. Exercise 23.11 · no public source solution
  12. Exercise 23.12 · no public source solution

D100:AK:24

Algebraic Curves · Unit 24: Lecture 24: Tangent Lines and Formal Power Series Rings

35 native section identities · 10 exercises · 1 complete solutions

10 exercises
  1. Exercise 24.1 · no public source solution
  2. Exercise 24.2 · no public source solution
  3. Exercise 24.3 · no public source solution
  4. Exercise 24.4 · complete solution
  5. Exercise 24.5 · no public source solution
  6. Exercise 24.6 · no public source solution
  7. Exercise 24.7 · no public source solution
  8. Exercise 24.8 · no public source solution
  9. Exercise 24.9 · no public source solution
  10. Exercise 24.10 · no public source solution

D100:AK:25

Algebraic Curves · Unit 25: Lecture 25: Power Series Solutions for Algebraic Curves

30 native section identities · 13 exercises · 2 complete solutions

13 exercises
  1. Exercise 25.1 · complete solution
  2. Exercise 25.2 · complete solution
  3. Exercise 25.3 · no public source solution
  4. Exercise 25.4 · no public source solution
  5. Exercise 25.5 · no public source solution
  6. Exercise 25.6 · no public source solution
  7. Exercise 25.7 · no public source solution
  8. Exercise 25.8 · no public source solution
  9. Exercise 25.9 · no public source solution
  10. Exercise 25.10 · no public source solution
  11. Exercise 25.11 · no public source solution
  12. Exercise 25.12 · no public source solution
  13. Exercise 25.13 · no public source solution

D100:AK:26

Algebraic Curves · Unit 26: Lecture 26: Intersection Multiplicity

38 native section identities · 11 exercises · 1 complete solutions

11 exercises
  1. Exercise 26.1 · no public source solution
  2. Exercise 26.2 · no public source solution
  3. Exercise 26.3 · no public source solution
  4. Exercise 26.4 · complete solution
  5. Exercise 26.5 · no public source solution
  6. Exercise 26.6 · no public source solution
  7. Exercise 26.7 · no public source solution
  8. Exercise 26.8 · no public source solution
  9. Exercise 26.9 · no public source solution
  10. Exercise 26.10 · no public source solution
  11. Exercise 26.11 · no public source solution

D100:AK:27

Algebraic Curves · Unit 27: Lecture 27: Projective Space

38 native section identities · 11 exercises · 0 complete solutions

11 exercises
  1. Exercise 27.1 · no public source solution
  2. Exercise 27.2 · no public source solution
  3. Exercise 27.3 · no public source solution
  4. Exercise 27.4 · no public source solution
  5. Exercise 27.5 · no public source solution
  6. Exercise 27.6 · no public source solution
  7. Exercise 27.7 · no public source solution
  8. Exercise 27.8 · no public source solution
  9. Exercise 27.9 · no public source solution
  10. Exercise 27.10 · no public source solution
  11. Exercise 27.11 · no public source solution

D100:AK:28

Algebraic Curves · Unit 28: Lecture 28: Projective Varieties and Projective Plane Curves

43 native section identities · 14 exercises · 1 complete solutions

14 exercises
  1. Exercise 28.1 · no public source solution
  2. Exercise 28.2 · no public source solution
  3. Exercise 28.3 · no public source solution
  4. Exercise 28.4 · no public source solution
  5. Exercise 28.5 · no public source solution
  6. Exercise 28.6 · no public source solution
  7. Exercise 28.7 · no public source solution
  8. Exercise 28.8 · no public source solution
  9. Exercise 28.9 · no public source solution
  10. Exercise 28.10 · complete solution
  11. Exercise 28.11 · no public source solution
  12. Exercise 28.12 · no public source solution
  13. Exercise 28.13 · no public source solution
  14. Exercise 28.14 · no public source solution

D100:AK:29

Algebraic Curves · Unit 29: Lecture 29: Projections and Parametrised Projective Curves

35 native section identities · 10 exercises · 2 complete solutions

10 exercises
  1. Exercise 29.1 · no public source solution
  2. Exercise 29.2 · complete solution
  3. Exercise 29.3 · complete solution
  4. Exercise 29.4 · no public source solution
  5. Exercise 29.5 · no public source solution
  6. Exercise 29.6 · no public source solution
  7. Exercise 29.7 · no public source solution
  8. Exercise 29.8 · no public source solution
  9. Exercise 29.9 · no public source solution
  10. Exercise 29.10 · no public source solution

D100:AK:30

Algebraic Curves · Unit 30: Lecture 30: Bézout's Theorem

34 native section identities · 12 exercises · 2 complete solutions

12 exercises
  1. Exercise 30.1 · no public source solution
  2. Exercise 30.2 · no public source solution
  3. Exercise 30.3 · complete solution
  4. Exercise 30.4 · complete solution
  5. Exercise 30.5 · no public source solution
  6. Exercise 30.6 · no public source solution
  7. Exercise 30.7 · no public source solution
  8. Exercise 30.8 · no public source solution
  9. Exercise 30.9 · no public source solution
  10. Exercise 30.10 · no public source solution
  11. Exercise 30.11 · no public source solution
  12. Exercise 30.12 · no public source solution

D100:BGK:01

Bundles, Sheaves and Cohomology · Unit 1: Lecture 1: Parameter-Dependent Systems of Linear Equations and Vector Bundles

3 native section identities · 17 exercises · 0 complete solutions

17 exercises
  1. Exercise 1.1 · no public source solution
  2. Exercise 1.2 · no public source solution
  3. Exercise 1.3 · no public source solution
  4. Exercise 1.4 · no public source solution
  5. Exercise 1.5 · no public source solution
  6. Exercise 1.6 · no public source solution
  7. Exercise 1.7 · no public source solution
  8. Exercise 1.8 · no public source solution
  9. Exercise 1.9 · no public source solution
  10. Exercise 1.10 · no public source solution
  11. Exercise 1.11 · no public source solution
  12. Exercise 1.12 · no public source solution
  13. Exercise 1.13 · no public source solution
  14. Exercise 1.14 · no public source solution
  15. Exercise 1.15 · no public source solution
  16. Exercise 1.16 · no public source solution
  17. Exercise 1.17 · no public source solution

D100:BGK:02

Bundles, Sheaves and Cohomology · Unit 2: Lecture 2: Sections, the Hairy Ball Theorem, and Gluing Data

3 native section identities · 27 exercises · 1 complete solutions

27 exercises
  1. Exercise 2.1 · no public source solution
  2. Exercise 2.2 · no public source solution
  3. Exercise 2.3 · no public source solution
  4. Exercise 2.4 · complete solution
  5. Exercise 2.5 · no public source solution
  6. Exercise 2.6 · no public source solution
  7. Exercise 2.7 · no public source solution
  8. Exercise 2.8 · no public source solution
  9. Exercise 2.9 · no public source solution
  10. Exercise 2.10 · no public source solution
  11. Exercise 2.11 · no public source solution
  12. Exercise 2.12 · no public source solution
  13. Exercise 2.13 · no public source solution
  14. Exercise 2.14 · no public source solution
  15. Exercise 2.15 · no public source solution
  16. Exercise 2.16 · no public source solution
  17. Exercise 2.17 · no public source solution
  18. Exercise 2.18 · no public source solution
  19. Exercise 2.19 · no public source solution
  20. Exercise 2.20 · no public source solution
  21. Exercise 2.21 · no public source solution
  22. Exercise 2.22 · no public source solution
  23. Exercise 2.23 · no public source solution
  24. Exercise 2.24 · no public source solution
  25. Exercise 2.25 · no public source solution
  26. Exercise 2.26 · no public source solution
  27. Exercise 2.27 · no public source solution

D100:BGK:03

Bundles, Sheaves and Cohomology · Unit 3: Lecture 3: Linear Constructions of Vector Bundles and Presheaves

3 native section identities · 18 exercises · 1 complete solutions

18 exercises
  1. Exercise 3.1 · complete solution
  2. Exercise 3.2 · no public source solution
  3. Exercise 3.3 · no public source solution
  4. Exercise 3.4 · no public source solution
  5. Exercise 3.5 · no public source solution
  6. Exercise 3.6 · no public source solution
  7. Exercise 3.7 · no public source solution
  8. Exercise 3.8 · no public source solution
  9. Exercise 3.9 · no public source solution
  10. Exercise 3.10 · no public source solution
  11. Exercise 3.11 · no public source solution
  12. Exercise 3.12 · no public source solution
  13. Exercise 3.13 · no public source solution
  14. Exercise 3.14 · no public source solution
  15. Exercise 3.15 · no public source solution
  16. Exercise 3.16 · no public source solution
  17. Exercise 3.17 · no public source solution
  18. Exercise 3.18 · no public source solution

D100:BGK:04

Bundles, Sheaves and Cohomology · Unit 4: Lecture 4: Sheaves and Sheaf Morphisms

3 native section identities · 9 exercises · 0 complete solutions

9 exercises
  1. Exercise 4.1 · no public source solution
  2. Exercise 4.2 · no public source solution
  3. Exercise 4.3 · no public source solution
  4. Exercise 4.4 · no public source solution
  5. Exercise 4.5 · no public source solution
  6. Exercise 4.6 · no public source solution
  7. Exercise 4.7 · no public source solution
  8. Exercise 4.8 · no public source solution
  9. Exercise 4.9 · no public source solution

D100:BGK:05

Bundles, Sheaves and Cohomology · Unit 5: Lecture 5: Sheafification, Homomorphisms and Quotient Sheaves

3 native section identities · 11 exercises · 1 complete solutions

11 exercises
  1. Exercise 5.1 · no public source solution
  2. Exercise 5.2 · no public source solution
  3. Exercise 5.3 · no public source solution
  4. Exercise 5.4 · no public source solution
  5. Exercise 5.5* · complete solution
  6. Exercise 5.6 · no public source solution
  7. Exercise 5.7 · no public source solution
  8. Exercise 5.8 · no public source solution
  9. Exercise 5.9 · no public source solution
  10. Exercise 5.10 · no public source solution
  11. Exercise 5.11 · no public source solution

D100:BGK:06

Bundles, Sheaves and Cohomology · Unit 6: Lecture 6: Exactness, Global Sections, and Pullback and Pushforward of Sheaves

3 native section identities · 19 exercises · 0 complete solutions

19 exercises
  1. Exercise 6.1 · no public source solution
  2. Exercise 6.2 · no public source solution
  3. Exercise 6.3 · no public source solution
  4. Exercise 6.4 · no public source solution
  5. Exercise 6.5 · no public source solution
  6. Exercise 6.6 · no public source solution
  7. Exercise 6.7 · no public source solution
  8. Exercise 6.8 · no public source solution
  9. Exercise 6.9 · no public source solution
  10. Exercise 6.10 · no public source solution
  11. Exercise 6.11 · no public source solution
  12. Exercise 6.12 · no public source solution
  13. Exercise 6.13 · no public source solution
  14. Exercise 6.14 · no public source solution
  15. Exercise 6.15 · no public source solution
  16. Exercise 6.16 · no public source solution
  17. Exercise 6.17 · no public source solution
  18. Exercise 6.18 · no public source solution
  19. Exercise 6.19 · no public source solution

D100:BGK:07

Bundles, Sheaves and Cohomology · Unit 7: Lecture 7: Ringed Spaces and Locally Ringed Spaces

3 native section identities · 21 exercises · 1 complete solutions

21 exercises
  1. Exercise 7.1 · no public source solution
  2. Exercise 7.2 · no public source solution
  3. Exercise 7.3 · no public source solution
  4. Exercise 7.4 · no public source solution
  5. Exercise 7.5 · no public source solution
  6. Exercise 7.6 · no public source solution
  7. Exercise 7.7 · no public source solution
  8. Exercise 7.8 · no public source solution
  9. Exercise 7.9 · no public source solution
  10. Exercise 7.10 · no public source solution
  11. Exercise 7.11 · no public source solution
  12. Exercise 7.12 · no public source solution
  13. Exercise 7.13 · no public source solution
  14. Exercise 7.14* · complete solution
  15. Exercise 7.15 · no public source solution
  16. Exercise 7.16 · no public source solution
  17. Exercise 7.17 · no public source solution
  18. Exercise 7.18 · no public source solution
  19. Exercise 7.19 · no public source solution
  20. Exercise 7.20 · no public source solution
  21. Exercise 7.21 · no public source solution

D100:BGK:08

Bundles, Sheaves and Cohomology · Unit 8: Lecture 8: The Spectrum of a Commutative Ring

3 native section identities · 22 exercises · 3 complete solutions

22 exercises
  1. Exercise 8.1 · no public source solution
  2. Exercise 8.2 · no public source solution
  3. Exercise 8.3* · complete solution
  4. Exercise 8.4* · complete solution
  5. Exercise 8.5 · no public source solution
  6. Exercise 8.6 · no public source solution
  7. Exercise 8.7 · no public source solution
  8. Exercise 8.8 · no public source solution
  9. Exercise 8.9 · no public source solution
  10. Exercise 8.10 · no public source solution
  11. Exercise 8.11* · complete solution
  12. Exercise 8.12 · no public source solution
  13. Exercise 8.13 · no public source solution
  14. Exercise 8.14 · no public source solution
  15. Exercise 8.15 · no public source solution
  16. Exercise 8.16 · no public source solution
  17. Exercise 8.17 · no public source solution
  18. Exercise 8.18 · no public source solution
  19. Exercise 8.19 · no public source solution
  20. Exercise 8.20 · no public source solution
  21. Exercise 8.21 · no public source solution
  22. Exercise 8.22 · no public source solution

D100:BGK:09

Bundles, Sheaves and Cohomology · Unit 9: Lecture 9: Affine Schemes

3 native section identities · 13 exercises · 0 complete solutions

13 exercises
  1. Exercise 9.1 · no public source solution
  2. Exercise 9.2 · no public source solution
  3. Exercise 9.3 · no public source solution
  4. Exercise 9.4 · no public source solution
  5. Exercise 9.5 · no public source solution
  6. Exercise 9.6 · no public source solution
  7. Exercise 9.7 · no public source solution
  8. Exercise 9.8 · no public source solution
  9. Exercise 9.9 · no public source solution
  10. Exercise 9.10 · no public source solution
  11. Exercise 9.11 · no public source solution
  12. Exercise 9.12 · no public source solution
  13. Exercise 9.13 · no public source solution

D100:BGK:11

Bundles, Sheaves and Cohomology · Unit 11: Lecture 11: Irreducible Spaces and Noetherian Schemes

3 native section identities · 19 exercises · 3 complete solutions

19 exercises
  1. Exercise 11.1 · no public source solution
  2. Exercise 11.2 · no public source solution
  3. Exercise 11.3 · no public source solution
  4. Exercise 11.4 · no public source solution
  5. Exercise 11.5 · no public source solution
  6. Exercise 11.6 · no public source solution
  7. Exercise 11.7 · no public source solution
  8. Exercise 11.8 · no public source solution
  9. Exercise 11.9* · complete solution
  10. Exercise 11.10 · no public source solution
  11. Exercise 11.11 · no public source solution
  12. Exercise 11.12 · no public source solution
  13. Exercise 11.13* · complete solution
  14. Exercise 11.14* · complete solution
  15. Exercise 11.15 · no public source solution
  16. Exercise 11.16 · no public source solution
  17. Exercise 11.17 · no public source solution
  18. Exercise 11.18 · no public source solution
  19. Exercise 11.19 · no public source solution

D100:BGK:12

Bundles, Sheaves and Cohomology · Unit 12: Lecture 12: The Projective Spectrum of a Graded Ring

3 native section identities · 19 exercises · 2 complete solutions

19 exercises
  1. Exercise 12.1 · no public source solution
  2. Exercise 12.2 · no public source solution
  3. Exercise 12.3 · no public source solution
  4. Exercise 12.4 · no public source solution
  5. Exercise 12.5 ★ · complete solution
  6. Exercise 12.6 · no public source solution
  7. Exercise 12.7 · no public source solution
  8. Exercise 12.8 · no public source solution
  9. Exercise 12.9 · no public source solution
  10. Exercise 12.10 ★ · complete solution
  11. Exercise 12.11 · no public source solution
  12. Exercise 12.12 · no public source solution
  13. Exercise 12.13 · no public source solution
  14. Exercise 12.14 · no public source solution
  15. Exercise 12.15 · no public source solution
  16. Exercise 12.16 · no public source solution
  17. Exercise 12.17 · no public source solution
  18. Exercise 12.18 · no public source solution
  19. Exercise 12.19 · no public source solution

D100:BGK:13

Bundles, Sheaves and Cohomology · Unit 13: Lecture 13: The Cone Map, Sheaves of Modules, and Invertible Sheaves

36 native section identities · 23 exercises · 0 complete solutions

23 exercises
  1. Exercise 13.1 · no public source solution
  2. Exercise 13.2 · no public source solution
  3. Exercise 13.3 · no public source solution
  4. Exercise 13.4 · no public source solution
  5. Exercise 13.5 · no public source solution
  6. Exercise 13.6 · no public source solution
  7. Exercise 13.7 · no public source solution
  8. Exercise 13.8 · no public source solution
  9. Exercise 13.9 · no public source solution
  10. Exercise 13.10 · no public source solution
  11. Exercise 13.11 · no public source solution
  12. Exercise 13.12 · no public source solution
  13. Exercise 13.13 · no public source solution
  14. Exercise 13.14 · no public source solution
  15. Exercise 13.15 · no public source solution
  16. Exercise 13.16 · no public source solution
  17. Exercise 13.17 · no public source solution
  18. Exercise 13.18 · no public source solution
  19. Exercise 13.19 · no public source solution
  20. Exercise 13.20 · no public source solution
  21. Exercise 13.21 · no public source solution
  22. Exercise 13.22 · no public source solution
  23. Exercise 13.23 · no public source solution

D100:BGK:14

Bundles, Sheaves and Cohomology · Unit 14: Lecture 14: Quasicoherent Modules

26 native section identities · 26 exercises · 0 complete solutions

26 exercises
  1. Exercise 14.1 · no public source solution
  2. Exercise 14.2 · no public source solution
  3. Exercise 14.3 · no public source solution
  4. Exercise 14.4 · no public source solution
  5. Exercise 14.5 · no public source solution
  6. Exercise 14.6 · no public source solution
  7. Exercise 14.7 · no public source solution
  8. Exercise 14.8 · no public source solution
  9. Exercise 14.9 · no public source solution
  10. Exercise 14.10 · no public source solution
  11. Exercise 14.11 · no public source solution
  12. Exercise 14.12 · no public source solution
  13. Exercise 14.13 · no public source solution
  14. Exercise 14.14 · no public source solution
  15. Exercise 14.15 · no public source solution
  16. Exercise 14.16 · no public source solution
  17. Exercise 14.17 · no public source solution
  18. Exercise 14.18 · no public source solution
  19. Exercise 14.19 · no public source solution
  20. Exercise 14.20 · no public source solution
  21. Exercise 14.21 · no public source solution
  22. Exercise 14.22 · no public source solution
  23. Exercise 14.23 · no public source solution
  24. Exercise 14.24 · no public source solution
  25. Exercise 14.25 · no public source solution
  26. Exercise 14.26 · no public source solution

D100:BGK:15

Bundles, Sheaves and Cohomology · Unit 15: Lecture 15: Modules on Projective Schemes

27 native section identities · 20 exercises · 0 complete solutions

20 exercises
  1. Exercise 15.1 · no public source solution
  2. Exercise 15.2 · no public source solution
  3. Exercise 15.3 · no public source solution
  4. Exercise 15.4 · no public source solution
  5. Exercise 15.5 · no public source solution
  6. Exercise 15.6 · no public source solution
  7. Exercise 15.7 · no public source solution
  8. Exercise 15.8 · no public source solution
  9. Exercise 15.9 · no public source solution
  10. Exercise 15.10 · no public source solution
  11. Exercise 15.11 · no public source solution
  12. Exercise 15.12 · no public source solution
  13. Exercise 15.13 · no public source solution
  14. Exercise 15.14 · no public source solution
  15. Exercise 15.15 · no public source solution
  16. Exercise 15.16 · no public source solution
  17. Exercise 15.17 · no public source solution
  18. Exercise 15.18 · no public source solution
  19. Exercise 15.19 · no public source solution
  20. Exercise 15.20 · no public source solution

D100:BGK:16

Bundles, Sheaves and Cohomology · Unit 16: Lecture 16: Locally Free Sheaves

24 native section identities · 23 exercises · 1 complete solutions

23 exercises
  1. Exercise 16.1 · no public source solution
  2. Exercise 16.2 · no public source solution
  3. Exercise 16.3 · no public source solution
  4. Exercise 16.4 · no public source solution
  5. Exercise 16.5 · no public source solution
  6. Exercise 16.6 · no public source solution
  7. Exercise 16.7 · no public source solution
  8. Exercise 16.8 · no public source solution
  9. Exercise 16.9 · no public source solution
  10. Exercise 16.10 · no public source solution
  11. Exercise 16.11 · no public source solution
  12. Exercise 16.12 ★ · complete solution
  13. Exercise 16.13 · no public source solution
  14. Exercise 16.14 · no public source solution
  15. Exercise 16.15 · no public source solution
  16. Exercise 16.16 · no public source solution
  17. Exercise 16.17 · no public source solution
  18. Exercise 16.18 · no public source solution
  19. Exercise 16.19 · no public source solution
  20. Exercise 16.20 · no public source solution
  21. Exercise 16.21 · no public source solution
  22. Exercise 16.22 · no public source solution
  23. Exercise 16.23 · no public source solution

D100:BGK:17

Bundles, Sheaves and Cohomology · Unit 17: Lecture 17: Geometric Vector Bundles

22 native section identities · 24 exercises · 0 complete solutions

24 exercises
  1. Exercise 17.1 · no public source solution
  2. Exercise 17.2 · no public source solution
  3. Exercise 17.3 · no public source solution
  4. Exercise 17.4 · no public source solution
  5. Exercise 17.5 · no public source solution
  6. Exercise 17.6 · no public source solution
  7. Exercise 17.7 · no public source solution
  8. Exercise 17.8 · no public source solution
  9. Exercise 17.9 · no public source solution
  10. Exercise 17.10 · no public source solution
  11. Exercise 17.11 · no public source solution
  12. Exercise 17.12 · no public source solution
  13. Exercise 17.13 · no public source solution
  14. Exercise 17.14 · no public source solution
  15. Exercise 17.15 · no public source solution
  16. Exercise 17.16 · no public source solution
  17. Exercise 17.17 · no public source solution
  18. Exercise 17.18 · no public source solution
  19. Exercise 17.19 · no public source solution
  20. Exercise 17.20 · no public source solution
  21. Exercise 17.21 · no public source solution
  22. Exercise 17.22 · no public source solution
  23. Exercise 17.23 · no public source solution
  24. Exercise 17.24 · no public source solution

D100:BGK:18

Bundles, Sheaves and Cohomology · Unit 18: Lecture 18: Kähler Differentials

38 native section identities · 25 exercises · 3 complete solutions

25 exercises
  1. Exercise 18.1 · no public source solution
  2. Exercise 18.2 · no public source solution
  3. Exercise 18.3 · no public source solution
  4. Exercise 18.4 · no public source solution
  5. Exercise 18.5 · no public source solution
  6. Exercise 18.6 ★ · complete solution
  7. Exercise 18.7 · no public source solution
  8. Exercise 18.8 · no public source solution
  9. Exercise 18.9 · no public source solution
  10. Exercise 18.10 · no public source solution
  11. Exercise 18.11 · no public source solution
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  13. Exercise 18.13 · no public source solution
  14. Exercise 18.14 · no public source solution
  15. Exercise 18.15 · no public source solution
  16. Exercise 18.16 · no public source solution
  17. Exercise 18.17 ★ · complete solution
  18. Exercise 18.18 ★ · complete solution
  19. Exercise 18.19 · no public source solution
  20. Exercise 18.20 · no public source solution
  21. Exercise 18.21 · no public source solution
  22. Exercise 18.22 · no public source solution
  23. Exercise 18.23 · no public source solution
  24. Exercise 18.24 · no public source solution
  25. Exercise 18.25 · no public source solution

D100:BGK:19

Bundles, Sheaves and Cohomology · Unit 19: Lecture 19: Tangent Bundles

29 native section identities · 12 exercises · 1 complete solutions

12 exercises
  1. Exercise 19.1 · no public source solution
  2. Exercise 19.2 · no public source solution
  3. Exercise 19.3 · no public source solution
  4. Exercise 19.4 · no public source solution
  5. Exercise 19.5 · no public source solution
  6. Exercise 19.6 · no public source solution
  7. Exercise 19.7 · no public source solution
  8. Exercise 19.8 · no public source solution
  9. Exercise 19.9 · no public source solution
  10. Exercise 19.10 ★ · complete solution
  11. Exercise 19.11 · no public source solution
  12. Exercise 19.12 · no public source solution

D100:BGK:20

Bundles, Sheaves and Cohomology · Unit 20: Lecture 20: The Picard Group

29 native section identities · 13 exercises · 0 complete solutions

13 exercises
  1. Exercise 20.1 · no public source solution
  2. Exercise 20.2 · no public source solution
  3. Exercise 20.3 · no public source solution
  4. Exercise 20.4 · no public source solution
  5. Exercise 20.5 · no public source solution
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  7. Exercise 20.7 · no public source solution
  8. Exercise 20.8 · no public source solution
  9. Exercise 20.9 · no public source solution
  10. Exercise 20.10 · no public source solution
  11. Exercise 20.11 · no public source solution
  12. Exercise 20.12 · no public source solution
  13. Exercise 20.13 · no public source solution

D100:BGK:21

Bundles, Sheaves and Cohomology · Unit 21: Lecture 21: Normal Schemes

23 native section identities · 13 exercises · 3 complete solutions

13 exercises
  1. Exercise 21.1 · no public source solution
  2. Exercise 21.2 · no public source solution
  3. Exercise 21.3 ★ · complete solution
  4. Exercise 21.4 · no public source solution
  5. Exercise 21.5 · no public source solution
  6. Exercise 21.6 · no public source solution
  7. Exercise 21.7 · no public source solution
  8. Exercise 21.8 · no public source solution
  9. Exercise 21.9 ★ · complete solution
  10. Exercise 21.10 ★ · complete solution
  11. Exercise 21.11 · no public source solution
  12. Exercise 21.12 · no public source solution
  13. Exercise 21.13 · no public source solution

D100:BGK:22

Bundles, Sheaves and Cohomology · Unit 22: Lecture 22: The Divisor Class Group

26 native section identities · 20 exercises · 1 complete solutions

20 exercises
  1. Exercise 22.1 · no public source solution
  2. Exercise 22.2 · no public source solution
  3. Exercise 22.3 · no public source solution
  4. Exercise 22.4 · no public source solution
  5. Exercise 22.5 · no public source solution
  6. Exercise 22.6 · no public source solution
  7. Exercise 22.7 · no public source solution
  8. Exercise 22.8 · no public source solution
  9. Exercise 22.9 · no public source solution
  10. Exercise 22.10 · no public source solution
  11. Exercise 22.11 · no public source solution
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  16. Exercise 22.16 · no public source solution
  17. Exercise 22.17 · no public source solution
  18. Exercise 22.18 · no public source solution
  19. Exercise 22.19 ★ · complete solution
  20. Exercise 22.20 · no public source solution

D100:BGK:23

Bundles, Sheaves and Cohomology · Unit 23: Lecture 23: Injective Modules

34 native section identities · 21 exercises · 0 complete solutions

21 exercises
  1. Exercise 23.1 · no public source solution
  2. Exercise 23.2 · no public source solution
  3. Exercise 23.3 · no public source solution
  4. Exercise 23.4 · no public source solution
  5. Exercise 23.5 · no public source solution
  6. Exercise 23.6 · no public source solution
  7. Exercise 23.7 · no public source solution
  8. Exercise 23.8 · no public source solution
  9. Exercise 23.9 · no public source solution
  10. Exercise 23.10 · no public source solution
  11. Exercise 23.11 · no public source solution
  12. Exercise 23.12 · no public source solution
  13. Exercise 23.13 · no public source solution
  14. Exercise 23.14 · no public source solution
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  17. Exercise 23.17 · no public source solution
  18. Exercise 23.18 · no public source solution
  19. Exercise 23.19 · no public source solution
  20. Exercise 23.20 · no public source solution
  21. Exercise 23.21 · no public source solution

D100:BGK:25

Bundles, Sheaves and Cohomology · Unit 25: Lecture 25: Sheaf Cohomology

24 native section identities · 13 exercises · 1 complete solutions

13 exercises
  1. Exercise 25.1 ★ · complete solution
  2. Exercise 25.2 · no public source solution
  3. Exercise 25.3 · no public source solution
  4. Exercise 25.4 · no public source solution
  5. Exercise 25.5 · no public source solution
  6. Exercise 25.6 · no public source solution
  7. Exercise 25.7 · no public source solution
  8. Exercise 25.8 · no public source solution
  9. Exercise 25.9 · no public source solution
  10. Exercise 25.10 · no public source solution
  11. Exercise 25.11 · no public source solution
  12. Exercise 25.12 · no public source solution
  13. Exercise 25.13 · no public source solution

D100:BGK:27

Bundles, Sheaves and Cohomology · Unit 27: Lecture 27: Cohomology on projective schemes

23 native section identities · 14 exercises · 0 complete solutions

14 exercises
  1. Exercise 27.1 · no public source solution
  2. Exercise 27.2 · no public source solution
  3. Exercise 27.3 · no public source solution
  4. Exercise 27.4 · no public source solution
  5. Exercise 27.5 · no public source solution
  6. Exercise 27.6 · no public source solution
  7. Exercise 27.7 · no public source solution
  8. Exercise 27.8 · no public source solution
  9. Exercise 27.9 · no public source solution
  10. Exercise 27.10 · no public source solution
  11. Exercise 27.11 · no public source solution
  12. Exercise 27.12 · no public source solution
  13. Exercise 27.13 · no public source solution
  14. Exercise 27.14 · no public source solution

D100:BGK:28

Bundles, Sheaves and Cohomology · Unit 28: Lecture 28: Morphisms to projective space

25 native section identities · 14 exercises · 1 complete solutions

14 exercises
  1. Exercise 28.1 · no public source solution
  2. Exercise 28.2 · no public source solution
  3. Exercise 28.3 · no public source solution
  4. Exercise 28.4 · no public source solution
  5. Exercise 28.5 · no public source solution
  6. Exercise 28.6 ★ · complete solution
  7. Exercise 28.7 · no public source solution
  8. Exercise 28.8 · no public source solution
  9. Exercise 28.9 · no public source solution
  10. Exercise 28.10 · no public source solution
  11. Exercise 28.11 · no public source solution
  12. Exercise 28.12 · no public source solution
  13. Exercise 28.13 · no public source solution
  14. Exercise 28.14 · no public source solution

D100:BGK:29

Bundles, Sheaves and Cohomology · Unit 29: Lecture 29: The genus of a curve

25 native section identities · 15 exercises · 2 complete solutions

15 exercises
  1. Exercise 29.1 · no public source solution
  2. Exercise 29.2 · no public source solution
  3. Exercise 29.3 · no public source solution
  4. Exercise 29.4 · no public source solution
  5. Exercise 29.5 ★ · complete solution
  6. Exercise 29.6 · no public source solution
  7. Exercise 29.7 · no public source solution
  8. Exercise 29.8 · no public source solution
  9. Exercise 29.9 · no public source solution
  10. Exercise 29.10 · no public source solution
  11. Exercise 29.11 · no public source solution
  12. Exercise 29.12 ★ · complete solution
  13. Exercise 29.13 · no public source solution
  14. Exercise 29.14 · no public source solution
  15. Exercise 29.15 · no public source solution

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Concentrated 19-unit mastery route

Fifty-seven items: 44 new editorial solutions and 13 references to existing public source solutions. These are not added to the source-exercise count.

  1. BGK 2: Stetiges Vektorfeld/S^2/Nur eine Nullstelle/Aufgabe/Lösung · existing_public_source_solution_reference
  2. BGK 2: New item 1 - Nowhere-zero sections and triviality of line bundles · new_editorial_solution
  3. BGK 2: New item 2 - The image of a section is a closed subspace · new_editorial_solution
  4. BGK 3: Kroneckerprodukt/2x2/Berechnung/Aufgabe/Lösung · existing_public_source_solution_reference
  5. BGK 3: New item 1 - The tensor square of the Möbius strip · new_editorial_solution
  6. BGK 3: New item 2 - Stalks of the product of two presheaves · new_editorial_solution
  7. BGK 4: New solution 1 - The product of two sheaves, Exercise 4.1 · new_editorial_solution
  8. BGK 4: New solution 2 - Sections on two disjoint pieces, Exercise 4.2 · new_editorial_solution
  9. BGK 4: New solution 3 - The skyscraper sheaf, Exercise 4.9 · new_editorial_solution
  10. BGK 5: Garbe/Untergarbe/Halmweise Zugehörigkeit/Aufgabe/Lösung · existing_public_source_solution_reference
  11. BGK 5: New solution 1 - The universal property of sheafification, Exercise 5.2 · new_editorial_solution
  12. BGK 5: New solution 2 - Stalks of a quotient sheaf, Exercise 5.11 · new_editorial_solution
  13. BGK 6: New item 1 - Brenner Exercise 6.4: a split sequence · new_editorial_solution
  14. BGK 6: New item 2 - Brenner Exercise 6.9: pushforward from a point · new_editorial_solution
  15. BGK 6: New item 3 - Brenner Exercise 6.13: the pullback–pushforward morphism bijection · new_editorial_solution
  16. BGK 7: Lokaler Ring/Restklassenring/Einheiten surjektiv/Aufgabe/Lösung · existing_public_source_solution_reference
  17. BGK 7: New item 1 - Brenner Exercise 7.5: the sheaf of units · new_editorial_solution
  18. BGK 7: New item 2 - Brenner Exercise 7.16: the residue field of continuous functions · new_editorial_solution
  19. BGK 8: Primideal/Charakterisierung als Kern nach Körper/Aufgabe/Lösung · existing_public_source_solution_reference
  20. BGK 8: Kommutative Ringtheorie/Primideal/Charakterisierung mit Restklassenring/Fakt/Beweis/Aufgabe/Lösung · existing_public_source_solution_reference
  21. BGK 8: Integre endlich erzeugte Algebren/Lokaler Isomorphismus/In Umgebung/Aufgabe/Lösung · existing_public_source_solution_reference
  22. BGK 9: 1. Localisation as a quotient ring · new_editorial_solution
  23. BGK 9: 2. When does a localisation vanish? · new_editorial_solution
  24. BGK 9: 3. Intermediate rings over a principal ideal domain · new_editorial_solution
  25. BGK 10: 1. Quasi-affine but not affine · new_editorial_solution
  26. BGK 10: 2. Quasi-affine but not quasi-compact · new_editorial_solution
  27. BGK 10: 3. Morphisms over a base and algebra homomorphisms · new_editorial_solution
  28. BGK 11: Differenzierbare Mannigfaltigkeit/Kette von abgeschlossenen Untermannigfaltigkeiten/Aufgabe/Lösung · existing_public_source_solution_reference
  29. BGK 11: Kommutativer Ring/Ideal/Endlich erzeugt/Überdeckungstest/Aufgabe/Lösung · existing_public_source_solution_reference
  30. BGK 11: Kommutativer Ring/Spektrum/Noethersches Schema/Aufgabe/Lösung · existing_public_source_solution_reference
  31. BGK 12: Projektive Ebene/Zwei Geraden/Schnittpunkt/1/Aufgabe/Lösung · existing_public_source_solution_reference
  32. BGK 12: Monomiales Ideal/Produkt/Erzeugergrad/Aufgabe/Lösung · existing_public_source_solution_reference
  33. BGK 12: New item 1: the coordinate cross yields two projective points · new_editorial_solution
  34. BGK 13: New item 1: the module structure on a stalk · new_editorial_solution
  35. BGK 13: New item 2: unit determinants and isomorphisms of free sheaves · new_editorial_solution
  36. BGK 13: New item 3: the dual of an invertible sheaf · new_editorial_solution
  37. BGK 14: New item 1: zero at a point, zero on a neighbourhood · new_editorial_solution
  38. BGK 14: New item 2: locally surjective, but not the unit ideal globally · new_editorial_solution
  39. BGK 14: New item 3: change of scalars and the tensor–Hom adjunction · new_editorial_solution
  40. BGK 15: 1. Different modules, the same projective sheaf · new_editorial_solution
  41. BGK 15: 2. Ten cubic sections on the projective plane · new_editorial_solution
  42. BGK 15: 3. Tensoring two twists adds their degrees · new_editorial_solution
  43. BGK 23: 1. Divisible as a group, but not injective as a module · new_editorial_solution
  44. BGK 23: 2. An injective resolution of length one for every commutative group · new_editorial_solution
  45. BGK 23: 3. The sheaf of all functions is flasque · new_editorial_solution
  46. BGK 24: Source Exercise 24.1: left exactness of Hom · new_editorial_solution
  47. BGK 24: Source Exercise 24.3: a projective module in the first argument · new_editorial_solution
  48. BGK 24: Source Exercise 24.4: Ext classes detected modulo k · new_editorial_solution
  49. BGK 25: Intervall/Intervallüberdeckung/2/Stetige Funktion/Differenz/Aufgabe/Lösung · existing_public_source_solution_reference
  50. BGK 25: Source Exercise 25.2: gluing representatives modulo continuous functions · new_editorial_solution
  51. BGK 25: Source Exercise 25.10: the sheaf of units and the function field · new_editorial_solution
  52. BGK 26: 1. Zeroth cohomology and the gluing axiom · new_editorial_solution
  53. BGK 26: 2. A constant sheaf on an irreducible space · new_editorial_solution
  54. BGK 26: 3. Solving a cocycle on two affine open sets · new_editorial_solution
  55. BGK 27: 1. Three monomial components in the Čech complex · new_editorial_solution
  56. BGK 27: 2. The module structure on monomials with all exponents negative · new_editorial_solution
  57. BGK 27: 3. Global sections on a plane curve · new_editorial_solution

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