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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| Main Authors: | , |
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| Format: | Article (Journal) |
| Language: | English |
| Published: |
15 September 2023
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| In: |
Advances in mathematics
Year: 2023, Volume: 429, Pages: 1-38 |
| ISSN: | 1090-2082 |
| DOI: | 10.1016/j.aim.2023.109183 |
| Online Access: | 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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| Author Notes: | Pengfei Huang, Hao Sun |
| Summary: | 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]. |
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| Item Description: | Online verfügbar: 29. Juni 2023 Gesehen am 17.08.2023 |
| Physical Description: | Online Resource |
| ISSN: | 1090-2082 |
| DOI: | 10.1016/j.aim.2023.109183 |