Vol. 13, No. 6, 2019

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

Volume 13
Issue 8, 1765–1981
Issue 7, 1509–1763
Issue 6, 1243–1507
Issue 5, 995–1242
Issue 4, 749–993
Issue 3, 531–747
Issue 2, 251–530
Issue 1, 1–249

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
Subscriptions
Editors' Interests
Submission Guidelines
Submission Form
Editorial Login
Ethics Statement
ISSN: 1944-7833 (e-only)
ISSN: 1937-0652 (print)
Author Index
To Appear
 
Other MSP Journals
The congruence topology, Grothendieck duality and thin groups

Alexander Lubotzky and Tyakal Nanjundiah Venkataramana

Vol. 13 (2019), No. 6, 1281–1298
DOI: 10.2140/ant.2019.13.1281
Abstract

This paper answers a question raised by Grothendieck in 1970 on the “Grothendieck closure” of an integral linear group and proves a conjecture of the first author made in 1980. This is done by a detailed study of the congruence topology of arithmetic groups, obtaining along the way, an arithmetic analogue of a classical result of Chevalley for complex algebraic groups. As an application we also deduce a group theoretic characterization of thin subgroups of arithmetic groups.

Keywords
congruence subgroup, thin groups
Mathematical Subject Classification 2010
Primary: 11E57
Secondary: 20G30
Milestones
Received: 8 May 2018
Revised: 20 January 2019
Accepted: 8 March 2019
Published: 18 August 2019
Authors
Alexander Lubotzky
Einstein Institute of Mathematics
The Hebrew University of Jerusalem
Israel
Tyakal Nanjundiah Venkataramana
School of Mathematics
Tata Institute of Fundamental Research
Mumbai
India