Integral $p$-adic non-abelian Hodge theory for small representations
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arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2023
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| _version_ | 1866908098334031872 |
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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 $\calO_C$ with rigid generic fiber $X$. In this paper, we construct a new period sheaf $\calO\widehat \bC_{\pd}^+$ on $X_{\proet}$ and use it to establish an integral $p$-adic Simspon correspondence for small $\OXp$-representations on $X_{\proet}$ and small Higgs bundles on $\frakX_{\et}$ which is compatible with the works on rational level. In particular, for a small $\OXp$-representations $\calL$ with induced Higgs bundle $(\calH,θ_{\calH})$, we provide a canonical morphism $\HIG(\calH,θ_{\calH})\to\rRν_*\calL$ with a uniformly bounded $p^{\infty}$-torsion cofiber. Finally, we shall use this canonical map to study an analogue of Deligne--Illusie decomposition with coefficients in small $\OXp$-representations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2304_07078 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Integral $p$-adic non-abelian Hodge theory for small representations Min, Yu Wang, Yupeng Algebraic Geometry 14G22, 14F30, 14G45 Let $\frakX$ be a smooth $p$-adic formal scheme over $\calO_C$ with rigid generic fiber $X$. In this paper, we construct a new period sheaf $\calO\widehat \bC_{\pd}^+$ on $X_{\proet}$ and use it to establish an integral $p$-adic Simspon correspondence for small $\OXp$-representations on $X_{\proet}$ and small Higgs bundles on $\frakX_{\et}$ which is compatible with the works on rational level. In particular, for a small $\OXp$-representations $\calL$ with induced Higgs bundle $(\calH,θ_{\calH})$, we provide a canonical morphism $\HIG(\calH,θ_{\calH})\to\rRν_*\calL$ with a uniformly bounded $p^{\infty}$-torsion cofiber. Finally, we shall use this canonical map to study an analogue of Deligne--Illusie decomposition with coefficients in small $\OXp$-representations. |
| title | Integral $p$-adic non-abelian Hodge theory for small representations |
| topic | Algebraic Geometry 14G22, 14F30, 14G45 |
| url | https://arxiv.org/abs/2304.07078 |