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

Fuente: arXiv
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Main Authors: Anschütz, Johannes, Heuer, Ben, Bras, Arthur-César Le
Format: Preprint
Published: 2022
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author Anschütz, Johannes
Heuer, Ben
Bras, Arthur-César Le
author_facet Anschütz, Johannes
Heuer, Ben
Bras, Arthur-César Le
contents 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.
format Preprint
id arxiv_https___arxiv_org_abs_2211_08470
institution arXiv
publishDate 2022
record_format arxiv
spellingShingle v-vector bundles on $p$-adic fields and Sen theory via the Hodge-Tate stack
Anschütz, Johannes
Heuer, Ben
Bras, Arthur-César Le
Number Theory
11S25, 11S20
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.
title v-vector bundles on $p$-adic fields and Sen theory via the Hodge-Tate stack
topic Number Theory
11S25, 11S20
url https://arxiv.org/abs/2211.08470