Morphisms of schemes
Selected full lessons supplying algebraic prerequisites for flat, smooth and étale morphisms.
- The diagonal and separated morphisms
- Finiteness of morphisms
- Limits of schemes and Noetherian approximation
- Affine morphisms, relative Spec, and finite morphisms
- Quasi-finite morphisms and Chevalley’s theorem
- Zariski's Main Theorem
Exact prerequisites · Attribution and licences
Further lessons
- Valuation rings and the valuative criterion of separatedness
- Proper morphisms and the valuative criterion of properness
- Very ample invertible sheaves, Segre and Veronese embeddings
- Ample invertible sheaves
- Projective morphisms and Chow’s lemma
- Dimension of fibres
- Normalization
- Rational maps and birational morphisms
- Effective Cartier divisors and invertible sheaves
- Blowing up
- Weil divisors and the class group