Study group on étale and crystalline cohomology

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.

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	-	-	Victor	Introduction: Zeta function and Weil Cohomologies
22 September	-	-	Alexander	Étale cohomology I: étale morphisms and Fundamental groups
29 September	-	-	Felix	Étale cohomology II: étale site and cohomology of sheaves
6 October	-	-	Paolo	Spectral sequences
13 October	-	-	-	Étale cohomology III: proper and smooth base change
20 October	-	-	-	Étale cohomology IV
27 October	-	-	-	Étale cohomology V
3 November	-	-	-	Intermezzo: Dwork's \(p\)-adic proof of rationality of \(\zeta\)-function
10 November	-	-	-	Algebraic de Rham cohomology: absolute and relative
17 November	-	-	-	Crystalline cohomology I : Crystalline site
24 November	-	-	-	Crystalline cohomology II : Crystalline cohomology and de Rham-Witt sequences
1 December	-	-	-	Crystalline cohomology III : Frobenius and F-isocrystals
8 December	-	-	-	Towards \(p\)-adic Hodge Theory: Comparison Theorems
15 December	-	-	-	Towards \(p\)-adic Hodge Theory: p-adic Galois representations

Main references

D. Arapura - An Introduction to Étale Cohomology
A. Ogus, P. Berthelot - Notes on Crystalline Cohomology
D. Kritz - Dwork's \(p\)-adic proof of rationality of \(\zeta\)-function (Notes for stage)
K.S. Kedlaya - Weil cohomology in practice
C.A. Weibel - An introduction to Homological Algebra