{"paper":{"title":"A structure theorem for subgroups of $GL_n$ over complete local Noetherian rings with large residual image","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NT"],"primary_cat":"math.RA","authors_text":"Jayanta Manoharmayum","submitted_at":"2013-04-03T21:49:40Z","abstract_excerpt":"Given a complete local Noetherian ring $(A,\\m_A)$ with finite residue field and a subfield $\\pmb{k}$ of $A/\\m_A$, we show that every closed subgroup $G$ of $GL_n(A)$ such that $G\\mod{\\m_A}\\supseteq SL_n(\\pmb{k})$ contains a conjugate of $SL_n(W(\\pmb{k})_A)$ under some small restrictions on $\\pmb{k}$. Here $W(\\pmb{k})_A$ is the closed subring of $A$ generated by the Teichm\\\"{u}ller lifts of elements of the subfield $\\pmb{k}$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1304.1196","kind":"arxiv","version":2},"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"}