{"paper":{"title":"Local-global principle for congruence subgroups of Chevalley groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RA","authors_text":"Alexei Stepanov, Himanee Apte","submitted_at":"2012-11-15T11:19:09Z","abstract_excerpt":"We prove Suslin's local-global principle for principal congruence subgroups of Chevalley groups. Let $G$ be a Chevalley--Demazure group scheme with a root system $\\Phi\\ne A_1$ and $E$ its elementary subgroup. Let $R$ be a ring and $I$ an ideal of $R$. Assume additionally that $R$ has no residue fields of 2 elements if $\\Phi=C_2$ or $G_2$.\n  Theorem. Let $g\\in G(R[X],XR[X])$. Suppose that for every maximal ideal $\\m$ of $R$ the image of $g$ under the localization homomorphism at $\\m$ belongs to $E(R_\\m[X],IR_\\m[X])$. Then, $g\\in E(R[X],IR[X])$.\n  The theorem is a common generalization of the re"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1211.3575","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"}