A p-adic Simpson correspondence for rigid analytic varieties

TL;DR

This paper develops a p-adic Simpson correspondence for rigid analytic varieties over orm, constructing a new period sheaf and extending previous work by Faltings and Liu-Zhu using cotangent complex theory.

Contribution

It introduces a novel p-adic Simpson correspondence for rigid analytic varieties with good reduction, utilizing cotangent complex techniques and constructing a new period sheaf.

Findings

Established a p-adic Simpson correspondence for rigid analytic varieties

Constructed a new period sheaf on the pro-étale site

Proved compatibility with previous foundational works

Abstract

In this paper, we establish a $p$-adic Simpson correspondence on the arena of Liu-Zhu for rigid analytic varieties $X$ over $\Cp$ with a liftable good reduction by constructing a new period sheaf on $X_{\proet}$. To do so, we use the theory of cotangent complex after Beilinson and Bhatt. Then we give an integral decompletion theorem and complete the proof by local calculations. Our construction is compatible with the previous works of Faltings and Liu-Zhu.