|Date: Thursday, April 06, 2017
Location: 1866 East Hall (4:10 PM to 5:30 PM)
Title: Integral etale cohomology of non-Archimedean analytic spaces
Abstract: In my work in progress on complex analytic vanishing cycles for formal schemes, I've defined integral "etale" cohomology groups of a compact strictly analytic space over the field of Laurent power series with complex coefficients. These are finitely generated abelian groups provided with a quasi-unipotent action of the fundamental group of the punctured complex plane, and they give rise to all l-adic etale cohomology groups of the space. After a short survey of this work, I'll explain a theorem which, in the case when the space is rig-smooth, compares those groups and the de Rham cohomology groups of the space. The latter are provided with the Gauss-Manin connection and an additional structure which allow one to recover from them the "etale" cohomology groups with complex coefficients.
Speaker: Vladimir Berkovich
Institution: Weizmann Institute of Science