On $p$-adic Simpson and Riemann-Hilbert correspondences in the imperfect residue field case
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2021
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| _version_ | 1866915232684703744 |
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| author | Gao, Hui |
| author_facet | Gao, Hui |
| contents | Let $K$ be a mixed characteristic complete discrete valuation field with residue field admitting a finite $p$-basis, and let $G_K$ be the Galois group. Inspired by Liu and Zhu's construction of $p$-adic Simpson and Riemann-Hilbert correspondences over rigid analytic varieties, we construct such correspondences for representations of $G_K$. As an application, we prove a Hodge-Tate (resp. de Rham) "rigidity" theorem for $p$-adic representations of $G_K$, generalizing a result of Morita. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2108_07029 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | On $p$-adic Simpson and Riemann-Hilbert correspondences in the imperfect residue field case Gao, Hui Number Theory Let $K$ be a mixed characteristic complete discrete valuation field with residue field admitting a finite $p$-basis, and let $G_K$ be the Galois group. Inspired by Liu and Zhu's construction of $p$-adic Simpson and Riemann-Hilbert correspondences over rigid analytic varieties, we construct such correspondences for representations of $G_K$. As an application, we prove a Hodge-Tate (resp. de Rham) "rigidity" theorem for $p$-adic representations of $G_K$, generalizing a result of Morita. |
| title | On $p$-adic Simpson and Riemann-Hilbert correspondences in the imperfect residue field case |
| topic | Number Theory |
| url | https://arxiv.org/abs/2108.07029 |