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Lectures on Étale Cohomology
Contents
Context
Cohomology
cohomology
Special and general types
Special notions
Variants
Operations
Theorems
Étale morphisms
This page collects links related to the book:
based on the textbook:
both on étale cohomology and the proof of the Weil conjectures.
Contents
I Basic theory
1. Introduction
2. Étale morphisms
3. The étale fundamental group
4. The local ring for the étale topology
5. Sites
6. Sheaves for the étale topology
7. The category of sheaves on
8. Direct and inverse image sheaves
9. Cohomology: Definition and basic properties
10. Cech cohomology
11. Principal homogeneous spaces and
12. Higher direct images; the Leray spectral sequence
13. The Weil-divisor exact sequence and the cohomology of
14. The cohomology of curves
15. Cohomological dimension
16. Purity; the Gysin sequence
17. The proper base change theorem
18. Cohomology groups with compact support
19. Finiteness theorem; Sheaves of -modules
20. The smooth base change theorem
21. The comparison theorem
23. The cycle map; Chern classes
24. Poincaré duality
II Proof of the Weil conjectures
26. The Weil conjecture
27. Proof of the Weil conjectures, except for the Riemann hypothesis
28. Preliminary reductions
30. The main lemma
31. The geometry of Lefschetz pencils
32. The cohomology of Lefschetz pencils
33. Completion of the proof of the Weil conjecture
34. The geometry of estimates
Last revised on February 25, 2023 at 09:34:04.
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