{"paper":{"title":"On the splitting fields of generic elements in Zariski dense subgroups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GR","math.SP"],"primary_cat":"math.NT","authors_text":"C. S. Rajan, Supriya Pisolkar","submitted_at":"2015-08-06T10:23:21Z","abstract_excerpt":"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 $K$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1508.01348","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}