Uniformization of \mathcal{G}bundles
Abstract
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 BruhatTits group scheme on C. In particular we prove the analog of the uniformization theorem of DrinfeldSimpson 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.
 Publication:

arXiv eprints
 Pub Date:
 November 2007
 arXiv:
 arXiv:0711.4450
 Bibcode:
 2007arXiv0711.4450H
 Keywords:

 Mathematics  Algebraic Geometry
 EPrint:
 25 pages, revised version