The goal is to study Etale Cohomology, with the hope to understand the definition of l-adic cohomology groups,
Grothendieck's sheaf-function dictionary, Lefschetz fixed point formula, and perhaps the sketch of the idea
of the proof of Weil conjectures by Deligne (though this is unlikely to be included in the seminar itself).
l-adic cohomology has wide applications in algebraic geometry, arithmetic geometry, number theory,
and representation theory of finite and p-adic groups (eg., character theory of finite groups of Lie type is stated entirely in these terms), and is also important for the formulation of the
geometric Langlands conjectures.
References, links, etc:
-
The main source at the beginning is J. Milne's notes.
-
G.Tamme, Introduction to etale cohomology
(through UBC
library)
- Freitag and Kiehl, "Etale cohomology and the Weil Conjecture" (available through Springerlink at the library website).
- Grothendieck Topologies, Notes on a seminar by M. Artin, 1962.
- Grothendieck's TOHOKU paper (on Project Euclid)
Part I ;
Part II
- Notes on character sheaves by Anne-Marie Aubert.
- Laumon's 1987 paper (at Numdam)
- Notes by Sug Woo Shin on sheaf-function correspondence.
- Two posts by Ben Webster on the secret blogging seminar:
Part I ;
Part II .
Talks:
- January 6: Organizational meeting (no mathematical content).
- January 13: Joel Friedman, sheaves on graphs and
preview (how to apply the notions of sheaves, cohomology, etc. to
discrete structures).
- January 20. Avi Kulkarni, Etale morphisms (reference: Milne, Section
2).
Avi started with a review of sheaf cohomology.
Notes
by Paul Garreett are a useful reference for that review, in
retrospect.
Avi's notes
- January 27. Talk 1: Avi continues with the example of ellptic curves.
Talk 2: Ed will start the discussion of etale fundamentale group.