A p-adic Simpson correspondence for rigid analytic varieties

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.