v-vector bundles on p-adic fields and Sen theory via the Hodge-Tate stack

Abstract

We describe the category of continuous semilinear representations and their cohomology for the Galois group of a p-adic field K with coefficients in a completed algebraic closure via vector bundles on the Hodge-Tate locus of the Cartier-Witt stack. This also gives a new perspective on classical Sen theory; for example it explains the appearance of an analogue of Colmez' period ring B Sen in a geometric way.