Moduli Spaces of Filtered G-local Systems on Curves

TL;DR

This paper constructs moduli spaces of filtered G-local systems on curves for any reductive group, establishing an algebraic framework that confirms the tame nonabelian Hodge correspondence for noncompact curves.

Contribution

It provides a new algebraic construction of Betti moduli spaces for filtered G-local systems, extending the nonabelian Hodge correspondence to noncompact curves.

Findings

Moduli spaces of filtered G-local systems are constructed algebraically.

The tame nonabelian Hodge correspondence is validated for these moduli spaces.

The results apply to arbitrary reductive groups over algebraically closed fields.

Abstract

In this paper, we construct the moduli spaces of filtered $G$-local systems on curves for an arbitrary reductive group $G$ over an algebraically closed field of characteristic zero. This provides an algebraic construction for the Betti moduli spaces in the tame nonabelian Hodge correspondence for vector bundles/principal bundles on noncompact curves. As a direct application, the tame nonabelian Hodge correspondence on noncompact curves holds not only for the relevant categories, but also for the moduli spaces.