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arXiv · 2512.21418

A $p$-adic Simpson correspondence for singular rigid-analytic varieties

Hanlin Cai·Zeyu Liu
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Abstract

Let $C$ be a complete, algebraically closed non-archimedean extension of $\mathbb{Q}_p$, and $X$ be a proper rigid-analytic variety over $C$. We show that the category of pro-\'etale vector bundles on $X$ is equivalent to the category of Higgs bundles on the $\eh$-site of $X$, thereby generalizing the work of Faltings and Heuer to arbitrary proper rigid-analytic varieties.

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Hanlin Cai, Zeyu Liu. 2025-12-24. A $p$-adic Simpson correspondence for singular rigid-analytic varieties. https://arxiv.org/abs/2512.21418

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