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Inventiones mathematicae

, Volume 192, Issue 3, pp 627–661 | Cite as

The Langlands-Kottwitz approach for some simple Shimura varieties

  • Peter Scholze
Article

Abstract

We show how the Langlands-Kottwitz method can be used to determine the semisimple local factors of the Hasse-Weil zeta-function of certain Shimura varieties. This is made possible by a new result describing part of the nearby cycle sheaves in certain situations. In combination with a general base-change lemma in harmonic analysis, we use this to prove a conjecture of Haines and Kottwitz for these Shimura varieties.

Keywords

Special Fibre Compact Open Subgroup Shimura Variety Parahoric Subgroup Principal Congruence Subgroup 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Notes

Acknowledgements

I thank my advisor M. Rapoport for introducing me to this area, his constant encouragement during the process of writing this paper, and his interest in these ideas. Moreover, I am grateful for the financial support of the Hausdorff Center for Mathematics in Bonn and the hospitality of the Institut Henri Poincaré, where part of this work was done.

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Copyright information

© Springer-Verlag 2012

Authors and Affiliations

  1. 1.Mathematisches Institut der Universität BonnBonnGermany

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