v-vector bundles on $p$-adic fields and Sen theory via the Hodge-Tate stack
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2022
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| _version_ | 1866917897297723392 |
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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 |