Complex conjugation and Shimura varieties

Blasius, Don; Guerberoff, Lucio

doi:10.2140/ant.2017.11.2289

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Complex conjugation and Shimura varieties

Don Blasius and Lucio Guerberoff

Vol. 11 (2017), No. 10, 2289–2321

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.

Keywords

Shimura varieties, conjugation, models

Mathematical Subject Classification 2010

Primary: 11G18

Secondary: 11G35, 11E57, 20G30

Milestones

Received: 21 February 2016

Revised: 30 March 2017

Accepted: 29 April 2017

Published: 31 December 2017

Authors

Don Blasius
Mathematics Department University of California, Los Angeles Los Angeles, CA United States

Lucio Guerberoff
Department of Mathematics University College London London United Kingdom

Vol. 11, No. 10, 2017