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 Glocal systems over X and G-Higgs bundles over the Frobenius twist X ′ with first order poles. To obtain a general statement of the correspondence, we introduce the language of parahoric group schemes to establish the correspondence.

Tame parahoric nonabelian Hodge correspondence on curves

“…Next, we define tame logahoric connections and tame logahoric D X -modules. Part of the material introduced here can be also found in [2,29]. We start by fixing G θ , a parahoric group scheme over X.…”