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

2022/11/15 by Johannes Anschütz, Ben Heuer, Anschütz, Johannes +3
Mathematics · #11S20 #11S25 #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2211.08470

openalex publication_date 2022/11/15 · openalex created_date 2022/11/25 · openalex updated_date 2026/08/02

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.

Citations

• P-adic Simpson correpondence via prismatic crystals
• Absolute prismatic cohomology
• Prismatization
• Hodge--Tate prismatic crystals and Sen theory

Related

• Vector bundles and p-adic representations I
• Line bundles and p-adic characters
• Some new directions in p-adic Hodge theory
• Multivariable p-adic Hodge theory for products of Galois groups
• Admissible pairs and p-adic Hodge structures I: Transcendence of the de Rham lattice