Étale cohomology seminar

The seminar meets on Thursdays at 10:15 in G 43.

Scheduled talks

23-05-19

Xiao Yang

Weil conjectures II (part 2)

Past talks

27-09-18

Organizational meeting

25-10-18

Sebastian Schlegel Mejia

01-11-18

Ole Ossen

08-11-18

Pascal Schilde

15-11-18

Lukas Scheiwiller

22-11-18

Shengxuan Liu

29-11-18

Yupei Xie

06-12-18

Noah Held

13-12-18

Alexandre Puttick

20-12-18

Paul Steinmann

21-02-19

Spectral sequences

28-02-19

Proper base change (introduction)

07-03-19

Emil Jacobsen

14-03-19

Xiao Yang

Constructible sheaves

28-03-19

Sebastian Schlegel Mejia

04-04-19

Yupei Xie

Proper base change III: devissage for morphisms (part 1)

11-04-19

Yupei Xie

Proper base change III: devissage for morphisms (part 2)

18-04-19

Lukas Scheiwiller

02-05-19

Nicolas Müller

09-05-19

Noah Held

16-05-19

Noah Held

Xiao Yang

Weil conjectures II (part 1)

Organizers

Max Mornev <maxim.mornev@math.ethz.ch>
Richard Pink <richard.pink@math.ethz.ch>

Approximate program

Left and right derived functors on abelian categories.

Étale morphisms.

The (big and small) étale site of a scheme.

Faithfully flat descent.

Cohomology of smooth projective curves over a separably closed field.

Proper base change.

Local acyclicity of smooth morphisms and smooth base change.

Boundedness of cohomology and preservation of constructibility under derived lower shriek.

Statement of Weil conjectures.

(Optional) Comparison with singular cohomology.

Primary sources

These are SGA 4 (three volumes), Deligne's SGA 4½ and SGA 5.

Théorie des topos et cohomologie étale des schémas. Séminaire de Géométrie Algébrique du Bois-Marie 1963–1964 (SGA 4). Dirigé par M. Artin, A. Grothendieck, et J. L. Verdier. Avec la collaboration de N. Bourbaki, P. Deligne et B. Saint-Donat. Lecture Notes in Mathematics 269, 270, 305. Springer-Verlag, Berlin-New York, 1972.
A properly typeset version is available at http://www.normalesup.org/~forgogozo/SGA4/tomes/SGA4.pdf

P. Deligne. Séminaire de Géométrie Algébrique du Bois Marie - Cohomologie étale. - SGA 4½. Lecture Notes in Mathematics, 569. Springer-Verlag, Berlin, 1977.
A properly typeset version is available at https://github.com/dkmiller/sga4.5

Cohomologie -adique et fonctions L. Séminaire de Géometrie Algébrique du Bois-Marie 1965–1966 (SGA 5). Edité par Luc Illusie. Lecture Notes in Mathematics 589. Springer-Verlag, Berlin-New York, 1977.

References

B. Bhatt. The étale topology. http://www-personal.umich.edu/~bhattb/math/etalestcksproj.pdf

E. Freitag, R. Kiehl. Étale cohomology and the Weil conjecture. Ergebnisse der Mathematik und ihrer Grenzgebiete (3), 13. Springer-Verlag, Berlin, 1988.

J.-P. Serre. Local fields. GTM 67. Springer-Verlag, New York-Berlin, 1979.

J.-P. Serre. Galois cohomology. Springer Monographs in Mathematics. Springer-Verlag, Berlin, 2002.

G. Tamme. Introduction to étale cohomology. Universitext. Springer-Verlag, Berlin, 1994.

Stacks Project authors. The Stacks Project. http://stacks.math.columbia.edu

Last modified: May 22, 2019.