Workshop is co-organized with Adrian Langer and it is a part of IMPANGA.

The aim of the workshop is the introduction into étale cohomology theory. The main source will be Arcata from SGA 4 1/2 (see here). One day before the proper workshop, on the 1st march (Thursday), there will be lectures for students and people who didn't have any or have little contact with étalness before.

The following materials might also be useful:

first of all lectures of Milne, but also

Milne "Étale cohomology"

Freitag, Kiehl "Étale cohomology and the Weil conjecture"

Lei Fu "Étale cohomology theory"

SGA 1

Here's the programme (might be slightly changed in the future)

1st march 2012 (preparatory lectures):

Lecture 1 (Jakub Witaszek) 10.15-11.45:

Definitions of flat, unramified, étale, smooth morphisms with examples and basic properties. Standard form of étale morphisms.

Lecture 2 (Joachim Jelisiejew) 12.00-13.30:

Local rings in étale topology and facts about henselian rings. Henselization.

Lecture 3 (Bartosz Naskręcki) 14.30-16.00:

Definitions of sites and sheaves with examples. Stalks.

2nd march 2012:

Lecture 1 (Agnieszka Bodzenta) 10.15-11.45:

Grothendieck topologies, sheaves, examples of topologies: Zariski, étale, fppf, fpqc. Definition of étale cohomology. Exact sequence of Kummer and Artin-Schreier.

Lecture 2 (Jakub Byszewski) 12.00-13.30:

Local rings in étale topology. Formalism of six operations on sheaves. Galois cohomology.

Lecture 3 (Przemysław Chojecki) 14.30-16.00:

Cohomology groups of curves.

3rd march 2012:

Lecture 4 (Adrian Langer) 10.15-11.45:

Fundamental group and applications.

Lecture 5 (Tomasz Maszczyk) 12.00-13.30:

Constructible sheaves and base change for proper morphisms.

Lecture 6 (Andrzej Weber) 14.30-16.00:

Poincaré duality.

Institut
Mathématique de Jussieu - Fondation Sciences Mathématiques de Paris -
Fédération de recherche Mathématiques Paris Centre