On a p-adic version of Narasimhan and Seshadri's theorem
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866909592812781568 |
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| author | Andreatta, Fabrizio |
| author_facet | Andreatta, Fabrizio |
| contents | Consider a smooth projective curve C of genus g over a complete discrete valuation field of characteristic 0 and residue field \Fbar_p. Motivated by Narasimhan and Seshadri's theorem, Faltings asked whether all semistable vector bundles of degree 0 over C_{\C_p} are in the image of the p-adic Simpson correspondence. Works of Deninger-Werner and Xu show that this is equivalent for the vector bundle to having potentially strongly semistable reduction. We prove that if C has good reduction, p>r(r-1) (g-1) and we consider a vector bundle of rank r with stable reduction, the conditions of having potentially strongly semistable reduction and of having strongly semistable reduction are equivalent. In particular, we provide a negative answer to Faltings' question |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_12766 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On a p-adic version of Narasimhan and Seshadri's theorem Andreatta, Fabrizio Algebraic Geometry Number Theory Consider a smooth projective curve C of genus g over a complete discrete valuation field of characteristic 0 and residue field \Fbar_p. Motivated by Narasimhan and Seshadri's theorem, Faltings asked whether all semistable vector bundles of degree 0 over C_{\C_p} are in the image of the p-adic Simpson correspondence. Works of Deninger-Werner and Xu show that this is equivalent for the vector bundle to having potentially strongly semistable reduction. We prove that if C has good reduction, p>r(r-1) (g-1) and we consider a vector bundle of rank r with stable reduction, the conditions of having potentially strongly semistable reduction and of having strongly semistable reduction are equivalent. In particular, we provide a negative answer to Faltings' question |
| title | On a p-adic version of Narasimhan and Seshadri's theorem |
| topic | Algebraic Geometry Number Theory |
| url | https://arxiv.org/abs/2406.12766 |