From the first announcement:
"The goal is to study Etale Cohomology, with the hope to understand
Grothendieck's sheaf-function dictionary, Lefschetz fixed point formula, and perhaps the idea of the proof
of Weil conjectures by Deligne (though this is unlikely to be included in the seminar itself).
The basic idea is that one can express functions on all kinds of spaces
(e.g., those arising in number theory), by means of geometry.
Thus, etale 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 automorphic forms.
For example, automorphic sheaves are the sheaf-theoretic
analogues of automorphic functions, via this sheaf-function dictionary, and are important in the formulation of the
geometric Langlands conjectures."
References, links, etc:
September 14. Masoud gave an overview/introduction to the idea of geometrization.
- September 22. Robert Klinzmann, introduction to sheaves I.
- September 29. Robert Klinzmann, introduction to sheaves and cohomology II.
- October 6. Alex Duncan, Introduction to Grothendieck topologies.
- October 13. Aurel Meyer, The etale fundamental group.
- October 20. STUDY BREAK (that is, no talk).
- October 27. Robert Klinzmann, TBA.
- Further topics:
- Sheaves of abelian groups on the etale site;
- Sheaves of $\Z_l$ and $\bar \Q_l$-modules;
- The formalism of 6 functors;
- Grothendieck-Lefschetz fixed point formula.
- Sheaf-function dictionary.
- All of the above already happened, in some order. Sorry about
neglecting this page.
- On December 1, I should finish the correspondence between characters
of abelian groups and character sheaves, and probably define
transform, following Laumon's paper. The rest is informal discussion.