Connections on parahoric torsors over curves

Abstract

We define parahoric $\cG$--torsors for certain Bruhat--Tits group scheme $\cG$ on a smooth complex projective curve $X$ when the weights are real, and also define connections on them. We prove that a $\cG$--torsor is given by a homomorphism from ${\pi }_1(X\setminus D)$ to a maximal compact subgroup of $G$, where $D\subset X$ is the parabolic divisor, if and only if the torsor is polystable.

arXiv commentTo appear in Publ.RIMS, Kyoto Univ