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Zariski density and genericity. (English) Zbl 1207.20045
The paper combines a number of results (some due to the author, some not) to show that Zariski density is, in a strong sense, a generic property of subgroups of \(\text{SL}(n,\mathbb{Z})\) and \(\text{Sp}(2n,\mathbb{Z})\). Theorem 4.1, stated as a joint result with Ilya Kapovich, asserts that a generic free group automorphism is hyperbolic.
The author is not careful with some statements. For example, in Remark 2.3, \(\mathbb{Z}_p\) probably means \(G(\mathbb{Z}_p\)). In Theorem 2.6, \(g_p\) should not be a scalar matrix.

20G35 Linear algebraic groups over adèles and other rings and schemes
22E40 Discrete subgroups of Lie groups
20H05 Unimodular groups, congruence subgroups (group-theoretic aspects)
20E07 Subgroup theorems; subgroup growth
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