Rivin, Igor Zariski density and genericity. (English) Zbl 1207.20045 Int. Math. Res. Not. 2010, No. 19, 3649-3657 (2010). 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. Reviewer: L. N. Vaserstein (University Park) Cited in 1 ReviewCited in 18 Documents MSC: 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 Keywords:Zariski dense subgroups; special linear groups; symplectic groups; complex algebraic groups; generic free group automorphisms PDFBibTeX XMLCite \textit{I. Rivin}, Int. Math. Res. Not. 2010, No. 19, 3649--3657 (2010; Zbl 1207.20045) Full Text: DOI