Uniformization of G-bundles

Abstract

We show some of the conjectures of Pappas and Rapoport concerning the moduli stack G-torsors on a curve C, where G is a semisimple Bruhat-Tits group scheme on C. In particular we prove the analog of the uniformization theorem of Drinfeld-Simpson in this setting. Furthermore we apply this to compute the connected components of these moduli stacks and to calculate the Picard group of BunG in case G is simply connected. © 2009 The Author(s).