Vol. 10, No. 9, 2016

Download this article
Download this article For screen
For printing
Recent Issues

Volume 14
Issue 9, 2295–2574
Issue 8, 2001–2294
Issue 7, 1669–1999
Issue 6, 1331–1667
Issue 5, 1055–1329
Issue 4, 815–1054
Issue 3, 545–813
Issue 2, 275–544
Issue 1, 1–274

Volume 13, 10 issues

Volume 12, 10 issues

Volume 11, 10 issues

Volume 10, 10 issues

Volume 9, 10 issues

Volume 8, 10 issues

Volume 7, 10 issues

Volume 6, 8 issues

Volume 5, 8 issues

Volume 4, 8 issues

Volume 3, 8 issues

Volume 2, 8 issues

Volume 1, 4 issues

The Journal
About the Journal
Editorial Board
Editors’ Interests
Submission Guidelines
Submission Form
Policies for Authors
Ethics Statement
ISSN: 1944-7833 (e-only)
ISSN: 1937-0652 (print)
Author Index
To Appear
Other MSP Journals
This article is available for purchase or by subscription. See below.
Galois-generic points on Shimura varieties

Anna Cadoret and Arno Kret

Vol. 10 (2016), No. 9, 1893–1934
DOI: 10.2140/ant.2016.10.1893

We discuss existence and abundance of Galois-generic points for adelic representations attached to Shimura varieties. First, we show that, for Shimura varieties of abelian type, -Galois-generic points are Galois-generic; in particular, adelic representations attached to such Shimura varieties admit (“lots of”) closed Galois-generic points. Next, we investigate further the distribution of Galois-generic points and show the André–Pink conjecture for them: if S is a connected Shimura variety associated to a -simple reductive group, then every infinite subset of the generalized Hecke orbit of a Galois-generic point is Zariski-dense in S. Our proof follows the approach of Pink for Siegel Shimura varieties. Our main contribution consists in showing that there are only finitely many Hecke operators of bounded degree on (adelic and connected) Shimura varieties. Compared with other approaches of this result, our proof, which relies on Bruhat–Tits theory, is effective and works for arbitrary Shimura varieties.

PDF Access Denied

However, your active subscription may be available on Project Euclid at

We have not been able to recognize your IP address as that of a subscriber to this journal.
Online access to the content of recent issues is by subscription, or purchase of single articles.

Please contact your institution's librarian suggesting a subscription, for example by using our journal-recom­mendation form. Or, visit our subscription page for instructions on purchasing a subscription.

You may also contact us at contact@msp.org
or by using our contact form.

Or, you may purchase this single article for USD 40.00:

Shimura varieties, Hecke orbits, Adelic representations of étale fundamental group, Galois generic points
Mathematical Subject Classification 2010
Primary: 11G18
Secondary: 20G35, 14F20
Received: 13 September 2015
Revised: 29 June 2016
Accepted: 12 August 2016
Published: 22 November 2016
Anna Cadoret
Centre de Mathématiques Laurent Schwartz
Ecole Polytechnique
91128 Palaiseau
Arno Kret
Faculty of Science
Korteweg–de Vries Instituut
Postbus 94248
1090 GE Amsterdam