Tame Parahoric Nonabelian Hodge Correspondence in Positive Characteristic over Algebraic Curves

2021/09/02 by Li, Mao, Sun, Hao
#14C30 #14D20 #14L15 #20G15 #Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2109.00850

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.

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