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Nearby cycles of automorphic étale sheaves

Part of: Discontinuous groups and automorphic forms Arithmetic algebraic geometry

Published online by Cambridge University Press:  05 October 2017

Kai-Wen Lan  and
Benoît Stroh
Kai-Wen Lan
Affiliation:
School of Mathematics, University of Minnesota, 127 Vincent Hall, 206 Church Street SE, Minneapolis, MN 55455, USA email [email protected]
Benoît Stroh
Affiliation:
C.N.R.S. and Université Paris 13, 99 avenue Jean Baptiste Clément, 99430 Villetaneuse, France email [email protected] Current address: C.N.R.S. and Institut de Mathématiques de Jussieu–Paris Rive Gauche, 4 place Jussieu, 75252 Paris Cedex 05, France
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Abstract

We show that the automorphic étale cohomology of a (possibly noncompact) PEL-type or Hodge-type Shimura variety in characteristic zero is canonically isomorphic to the cohomology of the associated nearby cycles over most of their mixed characteristics models constructed in the literature.

Keywords

integral models of Shimura varietiescompactificationsautomorphic étale sheavesnearby cycles

MSC classification

Primary: 11G18: Arithmetic aspects of modular and Shimura varieties
Secondary: 11G15: Complex multiplication and moduli of abelian varieties 11F75: Cohomology of arithmetic groups
Type
Research Article
Information
Compositio Mathematica , Volume 154 , Issue 1 , January 2018 , pp. 80 - 119
Copyright
© The Authors 2017 

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