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2017 Complex conjugation and Shimura varieties
Don Blasius, Lucio Guerberoff
Algebra Number Theory 11(10): 2289-2321 (2017). DOI: 10.2140/ant.2017.11.2289

Abstract

In this paper we study the action of complex conjugation on Shimura varieties and the problem of descending Shimura varieties to the maximal totally real field of the reflex field. We prove the existence of such a descent for many Shimura varieties whose associated adjoint group has certain factors of type A or D . This includes a large family of Shimura varieties of abelian type. Our considerations and constructions are carried out purely at the level of Shimura data and group theory.

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Don Blasius. Lucio Guerberoff. "Complex conjugation and Shimura varieties." Algebra Number Theory 11 (10) 2289 - 2321, 2017. https://doi.org/10.2140/ant.2017.11.2289

Information

Received: 21 February 2016; Revised: 30 March 2017; Accepted: 29 April 2017; Published: 2017
First available in Project Euclid: 1 February 2018

zbMATH: 06825451
MathSciNet: MR3744357
Digital Object Identifier: 10.2140/ant.2017.11.2289

Subjects:
Primary: 11G18
Secondary: 11E57 , 11G35 , 20G30

Keywords: conjugation , models , Shimura varieties

Rights: Copyright © 2017 Mathematical Sciences Publishers

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Vol.11 • No. 10 • 2017
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