Uniformization of \mathcal{G}-bundles

Details Uniformization of \mathcal{G}-bundles Uniformization of \mathcal{G}-bundles

2007-11-28

arxiv.org/abs/0711.4450v2

Mathematics

Algebraic Geometry

25 pages, revised version

Scientific paper

We show some of the conjectures of Pappas and Rapoport concerning the moduli stack of $\mathcal{G}$-torsors on a curve C, where $\mathcal{G}$ 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 the stack of torsors in case $\mathcal{G}$ is simply connected.

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