Syntomic complex and $p$-adic nearby cycles
Fuente:
arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2023
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| _version_ | 1866908688297492480 |
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| author | Abhinandan |
| author_facet | Abhinandan |
| contents | In local relative $p$-adic Hodge theory, we show that the Galois cohomology of a finite height crystalline representation (up to a twist) is essentially computed via the (Fontaine--Messing) syntomic complex with coefficients in the associated $F$-isocrystal. In global applications, for smooth ($p$-adic formal) schemes, we establish a comparison between the syntomic complex with coefficients in a locally free Fontaine--Laffaille module and the $p$-adic nearby cycles of the associated étale local system on the (rigid) generic fibre. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2308_10736 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Syntomic complex and $p$-adic nearby cycles Abhinandan Number Theory Algebraic Geometry 14F20, 14F30, 14F40, 11S25 In local relative $p$-adic Hodge theory, we show that the Galois cohomology of a finite height crystalline representation (up to a twist) is essentially computed via the (Fontaine--Messing) syntomic complex with coefficients in the associated $F$-isocrystal. In global applications, for smooth ($p$-adic formal) schemes, we establish a comparison between the syntomic complex with coefficients in a locally free Fontaine--Laffaille module and the $p$-adic nearby cycles of the associated étale local system on the (rigid) generic fibre. |
| title | Syntomic complex and $p$-adic nearby cycles |
| topic | Number Theory Algebraic Geometry 14F20, 14F30, 14F40, 11S25 |
| url | https://arxiv.org/abs/2308.10736 |