Some questions about $\mathcal G$-bundles on curves

Details Some questions about $\mathcal G$-bundles on curves Some questions about $\mathcal G$-bundles on curves

2008-08-27

arxiv.org/abs/0808.3743v2

Mathematics

Algebraic Geometry

11 pages, added some references to mathematical physics literature

Scientific paper

We define the notion of a parahoric group scheme $\mathcal G$ over a smooth projective curve, and formulate four conjectures on the structure of the stack of $\mathcal G$-bundles, which generalize to this case well-known results on $G$-bundles with $G$ a constant reductive group. The conjectures concern the set of connected components, the uniformization by affine flag varieties of twisted loop groups, the Picard groups, and the space of global sections of a dominant line bundle. Since a first version of this paper was circulated, Heinloth [arXiv:0711.4450] has proved a good part of these conjectures.

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