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

• Verfasst von: Huang, Pengfei [VerfasserIn]
• Verfasst von: Sun, Hao [VerfasserIn]
• Titel: Meromorphic parahoric Higgs torsors and filtered Stokes G-local systems on curves
• Verf.angabe: Pengfei Huang, Hao Sun
• E-Jahr: 2023
• Jahr: 15 September 2023
• Umfang: 38 S.
• Fussnoten: Online verfügbar: 29. Juni 2023 ; Gesehen am 17.08.2023
• Titel Quelle: Enthalten in: Advances in mathematics
• Ort Quelle: Amsterdam [u.a.] : Elsevier, 1961
• Jahr Quelle: 2023
• Band/Heft Quelle: 429(2023) vom: Sept., Artikel-ID 109183, Seite 1-38
• ISSN Quelle: 1090-2082
• DOI: doi:10.1016/j.aim.2023.109183
• Datenträger: Online-Ressource
• Sprache: eng
• Sach-SW: Meromorphic Higgs bundle
• Sach-SW: Meromorphic integrable connection
• Sach-SW: Stokes local system
• Sach-SW: Wild nonabelian Hodge correspondence
• K10plus-PPN: 1856430618

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 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].