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

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 c...

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Hauptverfasser: Huang, Pengfei (VerfasserIn) , Sun, Hao (VerfasserIn)
Dokumenttyp: Article (Journal)
Sprache:Englisch
Veröffentlicht: 15 September 2023
In: Advances in mathematics
Year: 2023, Jahrgang: 429, Pages: 1-38
ISSN:1090-2082
DOI:10.1016/j.aim.2023.109183
Online-Zugang:Verlag, lizenzpflichtig, Volltext: https://doi.org/10.1016/j.aim.2023.109183
Verlag, lizenzpflichtig, Volltext: https://www.sciencedirect.com/science/article/pii/S0001870823003262
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Verfasserangaben:Pengfei Huang, Hao Sun
Beschreibung
Zusammenfassung: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, §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). When G=GLn(C), the main result in this paper reduces to that in [4].
Beschreibung:Online verfügbar: 29. Juni 2023
Gesehen am 17.08.2023
Beschreibung:Online Resource
ISSN:1090-2082
DOI:10.1016/j.aim.2023.109183

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