Abstract
Let k be an algebraically closed field of arbitrary characteristic, let
Funding source: Deutsche Forschungsgemeinschaft
Award Identifier / Grant number: FG 1920
Award Identifier / Grant number: SPP 1489
Funding statement: Gebhard Böckle is supported by the DFG in the FG 1920 and by the DFG/FNR within the SPP 1489. Wojciech Gajda was supported by the Alexander von Humboldt Foundation and by the National Centre of Sciences of Poland under research grant UMO-2012/07/B/ST1/03541.
Acknowledgements
Gebhard Böckle thanks the Fields Institute for a research stay in the spring of 2012 during which part of this work was written. He also thanks Adam Mickiewicz University in Poznań for making possible a joint visit of the three authors in the fall of 2012. Wojciech Gajda thanks the Interdisciplinary Center for Scientific Computing (IWR) at Heidelberg University for hospitality during research visits in January 2012 and in January 2014. Sebastian Petersen thanks the Mathematics Department at Adam Mickiewicz University for hospitality and support during several research visits. We thank F. Orgogozo and L. Illusie for interesting correspondence concerning this project. In addition, the authors thank the anonymous referee for a thorough review of the paper and many helpful comments and suggestions, and in particular for pointing us to [Modular functions of one variable. II (Antwerp 1972), Lecture Notes in Math. 349, Springer, Berlin (1973), 501–597, Théorème 9.8] that replaced earlier arguments involving the global Langlands correspondence proven by L. Lafforgue.
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