The congruence topology, Grothendieck duality and thin groups
Group Theory
2017-09-20 v1
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
Cite
@article{arxiv.1709.06179,
title = {The congruence topology, Grothendieck duality and thin groups},
author = {Alexander Lubotzky and T. N. Venkataramana},
journal= {arXiv preprint arXiv:1709.06179},
year = {2017}
}
Comments
24 pages