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 $B_{\mathrm{Sen}}$ in a geometric way.

30 pages, comments welcome!

References in corpus (9)

• Absolute prismatic cohomology
• A p-adic Simpson correspondence for rigid analytic varieties
• The prismatization of $p$-adic formal schemes
• Line bundles on rigid spaces in the $v$-topology
• Prismatization
• Hodge--Tate prismatic crystals and Sen theory
• On the Hodge--Tate crystals over O_K
• A Fourier Transform for Banach-Colmez spaces
• P-adic Simpson correpondence via prismatic crystals

Cited by in corpus (1)

• The small $p$-adic Simpson correspondence in terms of moduli spaces