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 $X^{\prime }$. To obtain a full description of the correspondence for the noncompact case, we introduce the language of parahoric group schemes to establish the correspondence.

25 pages

References in corpus (2)

• Reduction theory for connections over the formal punctured disc
• The Poincare line bundle and autoduality of Hitchin fibers

Cited by in corpus (1)

• Tame parahoric nonabelian Hodge correspondence on curves