{"paper":{"title":"Le d\\'efaut d'approximation forte dans les groupes lin\\'eaires connexes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Cyril Demarche","submitted_at":"2009-06-18T14:38:46Z","abstract_excerpt":"Let G be a connected linear algebraic group over a number field k. We establish an exact sequence describing the closure of the group G(k) of rational points of G in the group of adelic points of G. This exact sequence describes the defect of strong approximation on G in terms of the algebraic Brauer group of G. In particular, we deduce from those results that the integral Brauer-Manin obstruction on a torsor under the group G is the only obstruction to the existence of an integral point on this torsor. We also obtain a non-abelian Poitou-Tate exact sequence for the Galois cohomology of the li"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0906.3456","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"}