A Nonabelian Hodge Correspondence for Principal Bundles in Positive Characteristic

2024/05/16 by Sheng Mao, Hao Sun, Sheng, Mao +3 · 1 citation
Mathematics · #14C30 #14L15 #20G15 #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #FOS: Mathematics #Finite Group Theory Research #Mathematics and Applications

paper · pdf · doi:10.48550/arxiv.2405.09947

openalex publication_date 2024/05/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we prove a nonabelian Hodge correspondence for principal bundles on a smooth variety X in positive characteristic, which generalizes the Ogus-Vologodsky correspondence for vector bundles. Then we extend the correspondence to logahoric torsors over a log pair (X,D), where D a reduced normal crossing divisor in X. As an intermediate step, we prove a correspondence between principal bundles on root stacks \mathscrX and parahoric torsors on (X,D), which generalizes the correspondence on curves given by Balaji--Seshadri to higher dimensional case.

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• Nonlinear Hodge correspondence in positive characteristic

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