## Algebraic Geometry Seminar: Rigid Cohomology for Algebraic Stacks

- Date: 04/12/2010

University of British Columbia

Rigid cohomology is one flavor of Weil

cohomology. This entails for instance that one can asociate to a scheme X

over F_p a collection of finite dimensional Q_p-vector spaces H^i(X)

(and variants with supports in a closed subscheme or compact support),

which enjoy lots and lots of nice properties (e.g. functorality,

excision, Gysin, duality, a trace formula -- basically everything one

needs to give a proof of the Weil conjectures).

Classically, the construction of rigid cohomology is a bit

complicated and requires many choices, so that proving things like

functorality (or even that it is well defined) are theorems in their own

right. An important recent advance is the construction by le Stum of an

`Overconvergent site' which computes the rigid cohomology of X. This

site involves no choices and so it trivially well defined, and many

things (like functorality) become transparent.

In this talk I'll explain a bit about classical rigid cohomology

and the overconvergent site, and explain some new work generalizing

rigid cohomology to algebraic stacks (as well as why one would want to

do such a thing).

TBA

3:00 - 4:00pm, WMAX 110.