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Study group on Weil cohomologies

The following page contains the information for a running study group in Fall 2025 in Leiden on étale and crystalline cohomology.
The seminar is organised by Paolo Bordignon, Alexander Molyakov, Felix Kalker and Victor de Vries.

consequence of Lefchetz trace formula

“[...] my work consists in deciphering a trilingual text; of each of the three columns I have only disparate fragments; I have some ideas about each of the three languages: but I know as well there are great differences in meaning from one column to another, for which nothing has prepared me in advance.”

— André Weil - March 26, 1940

Schedule and topics

This is a list of the 15 topics for the study group in preparation to a research seminar on Lawrence-Venkatesh methods that will follow in the second semester. Every talk should last between 90 and 120 minutes with a small break in the middle. We strongly encourage each speaker to provide examples and explicit computations.

Date

Time

Room

 Speaker Topic
15 September 13:15 - 15:00 BW 2.18a Paolo Introduction: Zeta function and Weil Cohomologies (notes)
22 September 13:15 - 15:00 BM 2.26 Felix Étale cohomology I: étale morphisms and Fundamental groups (notes)
29 September 13:15 - 15:00 BW 0.19 Alexander Étale cohomology II: étale site and cohomology of sheaves (notes)
6 October 13:15 - 15:00 BW 2.18a Victor Étale cohomology III: étale cohomology of curves (notes)
13 October 13:15 - 15:00 BW 2.18a Jorre Étale cohomology IV: Čech cohomology and cup product (notes)
20 October 13:15 - 15:00 DM 1.15 Amira Étale cohomology V: cycle classes and base change theorem
27 October 13:15 - 15:00 DM 1.15 Victor/Alexander Étale cohomology VI: main theorems and Weil conjectures I, II, III
3 November - - - no talk
10 November 13:15 - 15:00 BE 0.08 Felix Intermezzo: Dwork's \(p\)-adic proof of rationality of \(\zeta\)-function
17 November 13:15 - 15:00 BE 0.08 Sanskar Algebraic de Rham cohomology: absolute and relative
24 November 10:15 - 12:00 BM 2.26 Stef Gauss-Manin connection
1 December - - - no talk : PhD day
8 December 13:15 - 15:00 BE 0.08 Paolo Crystalline cohomology I : Crystalline site
15 December 13:15 - 15:00 BE 0.08 Paolo Crystalline cohomology II : de Rham-Witt complex
? January - - Paolo Deformation of Zeta functions for hyperelliptic curves
? January - - Alexander Hodge-Tate decomposition for \(p\)-divisible groups

Main references

Further readings