A p-adic Simpson correspondence for rigid analytic varieties

Wang, Yupeng

doi:10.2140/ant.2023.17.1453

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A p-adic Simpson correspondence for rigid analytic varieties

Yupeng Wang

Vol. 17 (2023), No. 8, 1453–1499

DOI: 10.2140/ant.2023.17.1453

Abstract

We establish a $p$ -adic Simpson correspondence in the spirit of Liu and Zhu for rigid analytic varieties $X$ over $ℂ_{p}$ with a liftable good reduction by constructing a new period sheaf on $X_{proét}$ . To do so, we use the theory of cotangent complexes described by 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 and Zhu.

Keywords

p-adic Simpson correspondence, period sheaf, small generalised representation, small Higgs bundles

Mathematical Subject Classification

Primary: 14F30, 14G22

Milestones

Received: 2 November 2021

Revised: 25 July 2022

Accepted: 6 September 2022

Published: 29 August 2023

Authors

Yupeng Wang
Morningside Center of Mathematics No. 505 Chinese Academy of Sciences Beijing China

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Vol. 17, No. 8, 2023