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

By J. Heinloth. 2007

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We show some of the conjectures of Pappas and Rapoport concerning the moduli stack $${{\rm Bun}_\mathcal {G}}$$ 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 $${{\rm Bun}_\mathcal {G}}$$ in case $${\mathcal {G}}$$ is simply connected.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/dd4f17d82a719b3e847da99b211b348786baa378