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Weil cohomology in practice
Kiran S. Kedlaya
Contents
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Contents
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Front Matter
1
Prehistory of the Weil conjectures
2
The Weil conjectures and examples
3
Weil's cohomological metaconjecture
4
Curves and abelian varieties
5
Two approaches to RH for curves
6
RH for abelian varieties
7
Inverse problems for zeta functions
8
The Lang–Weil estimate
9
Étale cohomology as a black box
10
Comparing Galois representations: the Faltings–Serre method
11
Dwork's proof of rationality
12
Algebraic de Rham cohomology
13
Monsky-Washnitzer cohomology
14
Frobenius actions and the Lefschetz–Monsky trace formula
15
Étale local systems
16
Étale fundamental groups
17
RH and Weil II
18
Causal versus random: the Tate conjecture and equidistribution
19
Exercises
Back Matter
Bibliography
Authored in PreTeXt
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https://kskedlaya.org/weil-cohom
©2019–2022 Kiran S. Kedlaya