Triviality properties of principal bundles on singular curves

Prakash Belkale, Najmuddin Fakhruddin

Published 2015-09-21Version 1

We show that principal bundles for a semisimple group on an arbitrary affine curve over an algebraically closed field are trivial, provided the order of $\pi_1$ of the group is invertible in the ground field, or if the curve has semi-normal singularities. Several consequences and extensions of this result (and method) are given.