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Mod $ p$ points on Shimura varieties of abelian type


Author: Mark Kisin
Journal: J. Amer. Math. Soc. 30 (2017), 819-914
MSC (2010): Primary 11G18; Secondary 11G10
DOI: https://doi.org/10.1090/jams/867
Published electronically: January 11, 2017
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Abstract: We show that the mod $ p$ points on a Shimura variety of abelian type with hyperspecial level have the form predicted by the conjectures of Kottwitz and Langlands-Rapoport. Along the way we show that the isogeny class of a mod $ p$ point contains the reduction of a special point.


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Additional Information

Mark Kisin
Affiliation: Department of Mathematics, Harvard University, 1 Oxford Street, Cambridge, Massachusetts 02138
Email: kisin@math.harvard.edu

DOI: https://doi.org/10.1090/jams/867
Keywords: Shimura varieties, Hodge cycles
Received by editor(s): September 9, 2013
Received by editor(s) in revised form: July 18, 2016
Published electronically: January 11, 2017
Additional Notes: The author was partially supported by NSF grant DMS-0017749000
Article copyright: © Copyright 2017 American Mathematical Society