nLab
Lectures on Étale Cohomology

Context

Cohomology

cohomology

Special and general types

Special notions

Variants

Extra structure

Operations

Theorems

Étale morphisms

This page collects links related to

based on the textbook

  • Étale Cohomology,

    Princeton Mathematical Series 33, 1980. xiii+323 pp.

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 X etX_{et}

8. Direct and inverse image sheaves

9. Cohomology: Definition and basic properties

10. Cech cohomology

11. Principal homogeneous spaces and H iH^i

12. Higher direct images; the Leray spectral sequence

13. The Weil-divisor exact sequence and the cohomology of 𝔾 m\mathbb{G}_m

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 l\mathbb{Z}_l-modules

20. The smooth base change theorem

21. The comparison theorem

22. The Künneth formula

23. The cycle map; Chern classes

24. Poincaré duality

25. Lefschetz fixed-point formula

II Proof of the Weil conjectures

26. The Weil conjecture

27. Proof of the Weil conjectures, except for the Riemann hypothesis

28. Preliminary reductions

29. The Lefschetz fixed point formula for non-constant sheaves

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

category: reference

Last revised on November 24, 2013 at 06:29:13. See the history of this page for a list of all contributions to it.