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arXiv · 2405.09947

A Nonabelian Hodge Correspondence for Principal Bundles in Positive Characteristic

Mao Sheng·Hao Sun·Jianping Wang
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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 $\mathscr{X}$ and parahoric torsors on $(X,D)$, which generalizes the correspondence on curves given by Balaji--Seshadri to higher dimensional case.

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Mao Sheng, Hao Sun, Jianping Wang. 2024-05-16. A Nonabelian Hodge Correspondence for Principal Bundles in Positive Characteristic. https://arxiv.org/abs/2405.09947

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