On the splitting fields of generic elements in Zariski dense subgroups

Let G be a connected, absolutely almost simple, algebraic group defined over a finitely generated, infinite field K, and let Γ be a Zariski dense subgroup of G(K). We show, apart from some few exceptions, that the commensurability class of the field F given by the compositum of the splitting fields...

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Bibliographic Details
Published in:Journal of algebra 2016-07, Vol.457, p.106-128
Main Authors: Pisolkar, Supriya, Rajan, C.S.
Format: Article
Language:English
Subjects:
Group theory
Representations of Lie groups
Weil groups of Lie groups
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Summary:Let G be a connected, absolutely almost simple, algebraic group defined over a finitely generated, infinite field K, and let Γ be a Zariski dense subgroup of G(K). We show, apart from some few exceptions, that the commensurability class of the field F given by the compositum of the splitting fields of characteristic polynomials of generic elements of Γ determines the group G up to isogeny over the algebraic closure of K.
ISSN:0021-8693
1090-266X
DOI:10.1016/j.jalgebra.2016.02.022