Tame Parahoric Nonabelian Hodge Correspondence in Positive Characteristic over Algebraic Curves

Abstract

Let $G$ be a reductive group, and let $X$ be an algebraic curve over an algebraically closed field $k$ with positive characteristic. We prove a version of nonabelian Hodge correspondence for tame $G$-local systems over $X$ and logarithmic $G$-Higgs bundles over the Frobenius twist $X'$. To obtain a full description of the correspondence for the noncompact case, we introduce the language of parahoric group schemes to establish the correspondence.