{"paper":{"title":"On Tate-Shafarevich groups of 1-motives over Galois extensions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Cristian D. Gonzalez-Aviles","submitted_at":"2015-09-04T00:48:23Z","abstract_excerpt":"Let K/F be a finite Galois extension of global fields with Galois group G and let M be a 1-motive over F. We discuss the kernel and cokernel of the restriction map Sha^{i}(F,M) --> Sha^{i}(K,M)^{G} for i=1 and 2, independently of any finiteness hypotheses. We show that these groups are finite and obtain, in particular, formulas for the corresponding quotient of group orders."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.01316","kind":"arxiv","version":3},"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"}