Meromorphic parahoric Higgs torsors and filtered Stokes G-lo cal systems on curves

作者：Huang, Pengfei^*; Sun, Hao

来源：Advances in Mathematics, 2023, 429: 109183.

DOI：10.1016/j.aim.2023.109183

• Wild nonabelian Hodge
• correspondence
• Meromorphic Higgs bundle
• Meromorphic integrable connection
• Stokes local system

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 on the irregular type of the meromorphic G-connections introduced by Boalch, and thus confirm a conjecture in [9, </n>1.5]. 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 G-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).