Faltings extension and Hodge-Tate filtration for abelian varieties over $p$-adic local fields with imperfect residue fields
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2020
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| _version_ | 1866909457213030400 |
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| author | He, Tongmu |
| author_facet | He, Tongmu |
| contents | Let $K$ be a complete discrete valuation field of characteristic $0$ with not necessarily perfect residue field of characteristic $p>0$. We define a Faltings extension of $\mathcal{O}_K$ over $\mathbb{Z}_p$, and we construct a Hodge-Tate filtration for abelian varieties over $K$ by generalizing Fontaine's construction in 1981, where he treated the perfect residue field case. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2003_09687 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | Faltings extension and Hodge-Tate filtration for abelian varieties over $p$-adic local fields with imperfect residue fields He, Tongmu Algebraic Geometry Number Theory 14F30, 14G20, 14K15 Let $K$ be a complete discrete valuation field of characteristic $0$ with not necessarily perfect residue field of characteristic $p>0$. We define a Faltings extension of $\mathcal{O}_K$ over $\mathbb{Z}_p$, and we construct a Hodge-Tate filtration for abelian varieties over $K$ by generalizing Fontaine's construction in 1981, where he treated the perfect residue field case. |
| title | Faltings extension and Hodge-Tate filtration for abelian varieties over $p$-adic local fields with imperfect residue fields |
| topic | Algebraic Geometry Number Theory 14F30, 14G20, 14K15 |
| url | https://arxiv.org/abs/2003.09687 |