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arXiv · 1709.06179

The congruence topology, Grothendieck duality and thin groups

Alexander Lubotzky·T. N. Venkataramana
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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, T. N. Venkataramana. 2017-09-18. The congruence topology, Grothendieck duality and thin groups. https://arxiv.org/abs/1709.06179

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