Moduli spaces of filtered G-local systems on curves

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.