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Computing integrals via cohomology

SPEAKER: Vadim Vologodsky

TITLE: Computing integrals via cohomology. (Joint work with Allen Stewart)

ABSTRACT: The Grothendieck-Lefschetz formula expresses the number of points on a variety over a finite field in terms of its cohomology groups equipped with the Frobenius action. We consider varieties over the field of p-adic numbers. In this case the number of points is usually infinite, but a top degree differential form on such a variety defines a measure on the set of its Q_p-points. Thus, one can talk about the volume of this set. Our problem is to find a cohomological formula for the volume, similar to the Grothendieck-Lefschetz formula. We will discuss some results in this direction.