{"paper":{"title":"A classification of torsors over Laurent polynomial rings","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RA","authors_text":"Arturo Pianzola, ICJ), Philippe Gille (IMAR, Vladimir Chernousov","submitted_at":"2015-10-19T19:00:32Z","abstract_excerpt":"Let R\\_n be the ring of Laurent polynomials in n variables  over a field k of characteristic zero and let K\\_n be its fraction field.Given a linear  algebraic k-group  $G$, we show that a K\\_n-torsor under G which is  unramified with respect to X=Spec(R\\_n)extends to a unique toral R\\_n-torsor under G. This result, in turn, allows us  to classify all G-torsors over R\\_n."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.05621","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"}