The small $p$-adic Simpson correspondence in the semi-stable reduction case
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866917801826975744 |
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| author | Sheng, Mao Wang, Yupeng |
| author_facet | Sheng, Mao Wang, Yupeng |
| contents | We generalize several known results on small Simpson correspondence for smooth formal schemes over $\calO_C$ to the case for semi-stable formal schemes. More precisely, for a liftable semi-stable formal scheme $\frakX$ over $\calO_C$ with generic fiber $X$, we establish (1) an equivalence between the category of Hitchin-small integral $v$-bundles on $X_{v}$ and the category of Hitchin-small Higgs bundles on $\frakX_{\et}$, generalizing the previous work of Min--Wang, and (2) an equivalence between the moduli stack of $v$-bundles on $X_{v}$ and the moduli stack of rational Higgs bundles on $\frakX_{\et}$ (equivalently, moduli stack of Higgs bundles on $X_{\et}$), generalizing the previous work of Anschütz--Heuer--Le Bras. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2410_09685 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The small $p$-adic Simpson correspondence in the semi-stable reduction case Sheng, Mao Wang, Yupeng Algebraic Geometry Number Theory We generalize several known results on small Simpson correspondence for smooth formal schemes over $\calO_C$ to the case for semi-stable formal schemes. More precisely, for a liftable semi-stable formal scheme $\frakX$ over $\calO_C$ with generic fiber $X$, we establish (1) an equivalence between the category of Hitchin-small integral $v$-bundles on $X_{v}$ and the category of Hitchin-small Higgs bundles on $\frakX_{\et}$, generalizing the previous work of Min--Wang, and (2) an equivalence between the moduli stack of $v$-bundles on $X_{v}$ and the moduli stack of rational Higgs bundles on $\frakX_{\et}$ (equivalently, moduli stack of Higgs bundles on $X_{\et}$), generalizing the previous work of Anschütz--Heuer--Le Bras. |
| title | The small $p$-adic Simpson correspondence in the semi-stable reduction case |
| topic | Algebraic Geometry Number Theory |
| url | https://arxiv.org/abs/2410.09685 |