Algebraic Geometry Seminar: Rigid Cohomology for Algebraic Stacks

  • Date: 04/12/2010
David Brown (UC-Berkeley)

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). 




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