This is a seminar jointly organized by Dimitri Ara
and Moritz Groth
. If you are interested
in participating in it (also for credits if desired), please send an email to
one of the organizers. The seminar will begin in the second week of October and
take place once a week.
This is the first part of a seminar on étale cohomology and its application to the Weil conjectures.
In the introduction of SGA 4˝, Deligne writes "The study of curves is the key
to etale cohomology." Taking this statement as a guideline, the aim of the
first part of this seminar will be to compute étale cohomogy groups of
curves. We will essentially take the shortest road towards these computations.
The general theorems of étale cohomology will be dealt with in the second part
of the seminar.
No knowledge of topos theory or étale cohomology is
assumed. We will try to recall all the scheme theoric notions (and in
particular the notion of a scheme). Nevertheless, some background in algebraic
geometry might help the participants.
The tentative schedule of the first sessions is:
Talk 00, 22.10.13: Introductory talk (Dimitri Ara)
Talk 01, 29.10.13: Recap of scheme theory (Giovanni Caviglia)
Talk 02, 05.11.13: Some important classes of morphisms (Joost Nuiten)
Talk 03, 12.11.13: Étale morphisms (Frank Rouman)
19.11.13: No seminar
Talk 04, 26.11.13: The étale site and étale cohomology (Urs Schreiber)
Talk 05, 03.12.13: Étale cohomology of fields (Johan Commelin)
10.12.13: Holiday break
Talk 06, ??.01.13: The additive group scheme and the Artin-Schreier sequence (Matan Prezma)
Talk 07: Brauer groups
Talk 08: The multiplicative group scheme and the Kummer sequence
Talk 09: Henselian rings
Talk 10: Stalks of higher direct images
Talk 11: Recap of abelian varieties
Talk 12: Étale cohomology of curves
The main references for the seminar are the following books:
Deligne: Cohomology étale
Milne: Étale cohomology
Tamme: Introduction to Étale cohomology
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