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A p-adic Simpson correspondence for rigid analytic varieties

Yupeng Wang

Vol. 17 (2023), No. 8, 1453–1499
Abstract

We establish a p-adic Simpson correspondence in the spirit of Liu and Zhu for rigid analytic varieties X over 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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