$p$-adic Simpson correspondences for principal bundles in abelian settings
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arXiv
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| Format: | Preprint |
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2023
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| _version_ | 1866913741302398976 |
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| author | Heuer, Ben Werner, Annette Zhang, Mingjia |
| author_facet | Heuer, Ben Werner, Annette Zhang, Mingjia |
| contents | We explore generalizations of the $p$-adic Simpson correspondence on smooth proper rigid spaces to principal bundles under rigid group varieties $G$. For commutative $G$, we prove that such a correspondence exists if and only if the Lie group logarithm is surjective. Second, we treat the case of general $G$ when $X$ is itself an ordinary abelian variety, in which case we prove a generalisation of Faltings' ``small'' correspondence to general rigid groups. On abeloid varieties, we also prove an analog of the classical Corlette-Simpson correspondence for principal bundles under linear algebraic groups. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2308_13456 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | $p$-adic Simpson correspondences for principal bundles in abelian settings Heuer, Ben Werner, Annette Zhang, Mingjia Algebraic Geometry 14G22, 14G45, 14F06 We explore generalizations of the $p$-adic Simpson correspondence on smooth proper rigid spaces to principal bundles under rigid group varieties $G$. For commutative $G$, we prove that such a correspondence exists if and only if the Lie group logarithm is surjective. Second, we treat the case of general $G$ when $X$ is itself an ordinary abelian variety, in which case we prove a generalisation of Faltings' ``small'' correspondence to general rigid groups. On abeloid varieties, we also prove an analog of the classical Corlette-Simpson correspondence for principal bundles under linear algebraic groups. |
| title | $p$-adic Simpson correspondences for principal bundles in abelian settings |
| topic | Algebraic Geometry 14G22, 14G45, 14F06 |
| url | https://arxiv.org/abs/2308.13456 |