Local cohomology, Lefschetz theorems and purity

Local cohomology and duality, connectedness, formal geometry, Lefschetz comparison, Picard groups, purity and specialization. All eight lessons include proofs, examples and solved exercises.

1. Local cohomology
2. Local duality and finiteness
3. Cohomological dimension, vanishing and connectedness
4. Formal geometry along a closed subscheme
5. Lefschetz theorems for finite étale covers
6. Picard groups and Grothendieck–Lefschetz
7. Purity of the branch locus
8. Specialization and tame ramification

Original text CC0 1.0 unless the lesson states other terms.