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arXiv · 2403.04565

On the Unipotent $p$-adic Simpson Correspondence

Thiago Solovera e Nery
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Abstract

The goal of this paper is to show a (derived) $p$-adic Simpson correspondence for (locally) unipotent coefficients on smooth rigid-analytic varieties. Our results depend on a deformation to $\mathbf{B}_\mathtt{dr}^+/\xi^2$, and not on a choice of exponential (as required for more general coefficients). Our methods are inherently higher categorical, hinging on the theory of modules over $\mathbf{E}_\infty$-algebras.

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Thiago Solovera e Nery. 2024-03-07. On the Unipotent $p$-adic Simpson Correspondence. https://arxiv.org/abs/2403.04565

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