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

Hanlin Cai; Zeyu Liu

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

Algebraic Geometry 2026-05-15 v2

Authors: Hanlin Cai , Zeyu Liu

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.

Keywords

p-adic hodge theory vector bundles and cohomology vector bundles

Cite

@article{arxiv.2512.21418,
  title  = {A $p$-adic Simpson correspondence for singular rigid-analytic varieties},
  author = {Hanlin Cai and Zeyu Liu},
  journal= {arXiv preprint arXiv:2512.21418},
  year   = {2026}
}

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