On Fontaine's conjecture for torsion crystalline local systems
Fuente:
arXiv
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866913463422418944 |
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| author | Moon, Yong Suk |
| author_facet | Moon, Yong Suk |
| contents | Let $\mathfrak{X}$ be a smooth connected $p$-adic formal scheme. Based on the prismatic description of crystalline local systems, we prove an analogue of Fontaine's conjecture for torsion crystalline local systems on the generic fiber of $\mathfrak{X}$. As an application, we show that the locus of crystalline local systems whose Hodge-Tate weights lie in a fixed interval cuts out a closed subscheme of the universal deformation ring. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2304_00855 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | On Fontaine's conjecture for torsion crystalline local systems Moon, Yong Suk Number Theory Algebraic Geometry Let $\mathfrak{X}$ be a smooth connected $p$-adic formal scheme. Based on the prismatic description of crystalline local systems, we prove an analogue of Fontaine's conjecture for torsion crystalline local systems on the generic fiber of $\mathfrak{X}$. As an application, we show that the locus of crystalline local systems whose Hodge-Tate weights lie in a fixed interval cuts out a closed subscheme of the universal deformation ring. |
| title | On Fontaine's conjecture for torsion crystalline local systems |
| topic | Number Theory Algebraic Geometry |
| url | https://arxiv.org/abs/2304.00855 |