Computing Congruence Quotients of Zariski Dense Subgroups

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Date
2018-10-26MFO Scientific Program
Research in Pairs 2018Series
Oberwolfach Preprints;2018,22Author
Detinko, Alla
Flannery, Dane
Hulpke, Alexander
Metadata
Show full item recordOWP-2018-22
Abstract
We obtain a computational realization of the strong approximation theorem. That is, we develop algorithms to compute all congruence quotients modulo rational primes of a finitely generated Zariski dense group $H \leq \mathrm{SL}(n, \mathbb{Z})$ for $n \geq 2$. More generally, we are able to compute all congruence quotients of a finitely generated Zariski dense subgroup of $\mathrm{SL}(n, \mathbb{Q})$ for $n > 2$.