Algebra & Number Theory
- Algebra Number Theory
- Volume 13, Number 6 (2019), 1281-1298.
The congruence topology, Grothendieck duality and thin groups
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.
Algebra Number Theory, Volume 13, Number 6 (2019), 1281-1298.
Received: 8 May 2018
Revised: 20 January 2019
Accepted: 8 March 2019
First available in Project Euclid: 21 August 2019
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 11E57: Classical groups [See also 14Lxx, 20Gxx]
Secondary: 20G30: Linear algebraic groups over global fields and their integers
Lubotzky, Alexander; Venkataramana, Tyakal Nanjundiah. The congruence topology, Grothendieck duality and thin groups. Algebra Number Theory 13 (2019), no. 6, 1281--1298. doi:10.2140/ant.2019.13.1281. https://projecteuclid.org/euclid.ant/1566353008