Crystalline representations and Wach modules in the relative case
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arXiv
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| Format: | Preprint |
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2021
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| _version_ | 1866910835048185856 |
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| author | Abhinandan |
| author_facet | Abhinandan |
| contents | We study the notion of Wach modules in relative setting, generalizing the arithmetic case. Over an unramified base, for a $p$-adic representation admitting such structure, we examine the relationship between its relative Wach module and filtered $(φ, \partial)$-module. Moreover, we show that such a representation is crystalline (in the sense of Brinon), and one can recover its filtered $(φ, \partial)$-module from the relative Wach module. Conversely, for low Hodge-Tate weights $[0, p-2]$, we construct relative Wach modules from free relative Fontaine-Laffaille modules (in the sense of Faltings). |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2103_17097 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Crystalline representations and Wach modules in the relative case Abhinandan Number Theory 11F80, 11S25, 14F30 We study the notion of Wach modules in relative setting, generalizing the arithmetic case. Over an unramified base, for a $p$-adic representation admitting such structure, we examine the relationship between its relative Wach module and filtered $(φ, \partial)$-module. Moreover, we show that such a representation is crystalline (in the sense of Brinon), and one can recover its filtered $(φ, \partial)$-module from the relative Wach module. Conversely, for low Hodge-Tate weights $[0, p-2]$, we construct relative Wach modules from free relative Fontaine-Laffaille modules (in the sense of Faltings). |
| title | Crystalline representations and Wach modules in the relative case |
| topic | Number Theory 11F80, 11S25, 14F30 |
| url | https://arxiv.org/abs/2103.17097 |