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arXiv · 2212.04939

Meromorphic Parahoric Higgs Torsors and Filtered Stokes G-local Systems on Curves

Pengfei Huang·Hao Sun
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Abstract

In this paper, we consider the wild nonabelian Hodge correspondence for principal $G$-bundles on curves, where $G$ is a connected complex reductive group. We establish the correspondence under a ``very good" condition introduced by Boalch, and thus confirm one of his conjectures. We first give a version of Kobayashi--Hitchin correspondence, which induces a one-to-one correspondence between stable meromorphic parahoric Higgs torsors of degree zero (Dolbeault side) and stable meromorphic parahoric connections of degree zero (de Rham side). Then, by introducing a notion of stability condition on filtered Stokes local systems, we prove a one-to-one correspondence between stable meromorphic parahoric connections of degree zero (de Rham side) and stable filtered Stokes $G$-local systems of degree zero (Betti side). When $G={\rm GL}_n(\mathbb{C})$, the main result in this paper reduces to Biquad--Boalch's result.

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Pengfei Huang, Hao Sun. 2023-06-16. Meromorphic Parahoric Higgs Torsors and Filtered Stokes G-local Systems on Curves. https://arxiv.org/abs/2212.04939

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