Algebra/Topology seminar Emanuel Reinecke

Title: Relative Poincare duality in nonarchimedean geometry

Abstract: While the etale cohomology groups of Z/p-local systems on smooth rigid-analytic varieties over p-adic fields are in general hard to control, they become more tractable when the spaces are proper. For example, in this case they are finite-dimensional and satisfy Poincare duality. After reviewing some background in rigid geometry, I will explain a new proof of Poincare duality in this context. The argument is essentially diagrammatic and also works for more general spaces and in the relative setting. Along the way, I will sketch a novel construction of trace maps for any smooth morphism of rigid-analytic varieties. Joint work with Shizhang Li and Bogdan Zavyalov.