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arXiv · 1508.01348

On the splitting fields of generic elements in Zariski dense subgroups

Supriya Pisolkar·C. S. Rajan
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Abstract

Let $G$ be a connected, absolutely almost simple, algebraic group defined over a finitely generated, infinite field $K$, and let $\Gamma$ be a Zariski dense subgroup of $G(K)$. We show, apart from some few exceptions, that the commensurability class of the field $\mathcal{F}$ given by the compositum of the splitting fields of characteristic polynomials of generic elements of $\Gamma$ determines the group $G$ upto isogeny over the algebraic closure of $K$.

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Supriya Pisolkar, C. S. Rajan. 2015-08-06. On the splitting fields of generic elements in Zariski dense subgroups. https://arxiv.org/abs/1508.01348

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