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2019 The congruence topology, Grothendieck duality and thin groups
Alexander Lubotzky, Tyakal Nanjundiah Venkataramana
Algebra Number Theory 13(6): 1281-1298 (2019). 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.

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Alexander Lubotzky. Tyakal Nanjundiah Venkataramana. "The congruence topology, Grothendieck duality and thin groups." Algebra Number Theory 13 (6) 1281 - 1298, 2019. https://doi.org/10.2140/ant.2019.13.1281

Information

Received: 8 May 2018; Revised: 20 January 2019; Accepted: 8 March 2019; Published: 2019
First available in Project Euclid: 21 August 2019

zbMATH: 07103974
MathSciNet: MR3994565
Digital Object Identifier: 10.2140/ant.2019.13.1281

Subjects:
Primary: 11E57
Secondary: 20G30

Keywords: congruence subgroup , thin groups

Rights: Copyright © 2019 Mathematical Sciences Publishers

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Vol.13 • No. 6 • 2019
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