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arXiv · 2211.08470

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

Johannes Anschütz·Ben Heuer·Arthur-César Le Bras
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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.

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Johannes Anschütz, Ben Heuer, Arthur-César Le Bras. 2022-11-15. v-vector bundles on $p$-adic fields and Sen theory via the Hodge-Tate stack. https://arxiv.org/abs/2211.08470

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