{"paper":{"title":"Super-approximation, II: the p-adic and bounded power of square-free integers cases","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Alireza Salehi Golsefidy","submitted_at":"2016-02-01T07:06:09Z","abstract_excerpt":"Let $\\Omega$ be a finite symmetric subset of GL$_n(\\mathbb{Z}[1/q_0])$, and $\\Gamma:=\\langle \\Omega \\rangle$. Then the family of Cayley graphs $\\{{\\rm Cay}(\\pi_m(\\Gamma),\\pi_m(\\Omega))\\}_m$ is a family of expanders as $m$ ranges over fixed powers of square-free integers and powers of primes that are coprime to $q_0$ if and only if the connected component of the Zariski-closure of $\\Gamma$ is perfect. Some of the immediate applications, e.g. orbit equivalence rigidity, {\\em largeness} of certain $\\ell$-adic Galois representations, are also discussed."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1602.00409","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"}