Hodge-Tate decomposition for non-smooth rigid spaces

Abstract: Given a smooth projective variety over a $p$-adic field, its $p$-adic étale cohomology admits a natural Galois equivariant decomposition, called Hodge-Tate decomposition. The decomposition builds a connection between the underlying $p$-adic Galois representation and the cohomology of differentials, relating arithmetic and geometric information altogether. In this talk, we generalize Hodge-Tate decomposition to non-smooth rigid spaces, and show how to compute $p$-adic étale cohomology via cohomology of Deligne-Du Bois complexes.

commutative algebraalgebraic geometrynumber theory

Audience: researchers in the topic

Recent Advances in Modern p-Adic Geometry (RAMpAGe)

Series comments: The Zoom Meeting ID is: 995 3670 1681. The password for the series is: *The first three-digit prime*. Please visit the external homepage for notes and videos from past talks.