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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2022
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2201.08030 |
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| _version_ | 1866913456511254528 |
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| author | Min, Yu Wang, Yupeng |
| author_facet | Min, Yu Wang, Yupeng |
| contents | Let $\frakX$ be a smooth $p$-adic formal scheme over $\calO_K$ with adic generic fiber $X$. We obtain a global equivalence between the category $\Vect((\frakX)_{\Prism},\overline\calO_{\Prism}[\frac{1}{p}])$ of rational Hodge--Tate crystals on the absolute prismatic site $(\frakX)_{\Prism}$ and the category $\HIG^{\nil}_*(X)$ of enhanced Higgs bundles on $X$. Along the way, we construct an inverse Simpson functor from $\HIG^{\nil}_*(X)$ to the category $\Vect(X_{\proet},\widehat\calO_X)$ of generalised representations on $X$, which turns out to be fully faithful. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2201_08030 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | P-adic Simpson correpondence via prismatic crystals Min, Yu Wang, Yupeng Algebraic Geometry Let $\frakX$ be a smooth $p$-adic formal scheme over $\calO_K$ with adic generic fiber $X$. We obtain a global equivalence between the category $\Vect((\frakX)_{\Prism},\overline\calO_{\Prism}[\frac{1}{p}])$ of rational Hodge--Tate crystals on the absolute prismatic site $(\frakX)_{\Prism}$ and the category $\HIG^{\nil}_*(X)$ of enhanced Higgs bundles on $X$. Along the way, we construct an inverse Simpson functor from $\HIG^{\nil}_*(X)$ to the category $\Vect(X_{\proet},\widehat\calO_X)$ of generalised representations on $X$, which turns out to be fully faithful. |
| title | P-adic Simpson correpondence via prismatic crystals |
| topic | Algebraic Geometry |
| url | https://arxiv.org/abs/2201.08030 |