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Semistable Non Abelian Hodge theorem in positive characteristic

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arxiv 2310.09923 v3 pith:W6LHHYKU submitted 2023-10-15 math.AG

Andres Fernandez Herrero , Siqing Zhang This is my paper · ORCID
classification math.AG
keywords semistablebundlescharacteristicconnectionsflathiggsmodulimorphism
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abstract

In this paper, we show that for any reductive group $G$ the moduli space of semistable $G$-Higgs bundles on a curve in characteristic $p$ is a twisted form of the moduli space of semistable flat $G$-connections. This is the semistable version of a previous result of Chen-Zhu, and the $G$-bundle version of a previous result of de Cataldo-Groechenig-Zhang. As a consequence, we show that the Decomposition Theorem for the Hitchin morphism for $G$-Higgs bundles has the same shape as that for the de Rham-Hitchin morphism for flat $G$-connections.

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  1. Hitchin fibrations are Ng\^{o} fibrations

    math.AG 2025-02 conditional novelty 7.0 of 10

    For every split reductive group G, the Hitchin fibration in the canonical and logarithmic cases is an Ngô fibration, so its direct image splits into Ngô strings.

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