Abstract
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.
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Acknowledgements
I thank M. Rapoport for explaining the conjectures formulated in [21] to me and G. Harder for his explanations on Bruhat-Tits groups. I thank N. Naumann, a discussion with him on a related question in an arithmetic situation was the starting point for this article. Furthermore I am indebted to Y. Laszlo. He suggested many improvements on a previous approach to the main theorem of this article, in particular he suggested an argument helping to avoid the use of the strong approximation theorem and reduction to positive characteristics. I thank A. Schmitt his comments. I am indebted to the referee for many comments and corrections.
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Open Access This is an open access article distributed under the terms of the Creative Commons Attribution Noncommercial License (https://creativecommons.org/licenses/by-nc/2.0), which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited.