论文标题
曲线上的Meromororphic Parahoric Higgs Torsors和过滤的Stokes G-Local Systems
Meromorphic Parahoric Higgs Torsors and Filtered Stokes G-local Systems on Curves
论文作者
论文摘要
在本文中，我们考虑了曲线上的本金$ g $捆绑的野生nonabelian hodge通信，其中$ g $是连接的复杂还原组。我们在Boalch引入的``非常良好''条件下建立了对应关系，因此确认了他的一种猜想。我们首先给出了Kobayashi-Hitchin对应关系的版本，该版本诱导了稳定的Meromorormormormormormormormormorphic Parahoric Higgs torsors torsors torsors Zero Zero Zero Zero（侧面）和稳定的Meromolomormorphoric Connections（dep）的一对一对应关系。在过滤的局部系统上引入了稳定条件的概念，我们证明了稳定的零态帕拉克连接度零（de rham side）和稳定的过滤量之间的对应关系。到Biquad-Boalch的结果。
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.
