{"paper":{"title":"On the refined conjectures on Fitting ideals of Selmer groups of elliptic curves with supersingular reduction","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Chan-Ho Kim, Masato Kurihara","submitted_at":"2018-04-02T07:08:54Z","abstract_excerpt":"In this paper, we study the Fitting ideals of Selmer groups over finite subextensions in the cyclotomic $\\mathbb{Z}_p$-extension of $\\mathbb{Q}$ of an elliptic curve over $\\mathbb{Q}$. Especially, we present a proof of the \"weak main conjecture\" \\`{a} la Mazur and Tate for elliptic curves with good (supersingular) reduction at an odd prime $p$. We also prove the \"strong main conjecture\" suggested by the second named author under the validity of the $\\pm$-main conjecture and the vanishing of a certain error term. The key idea is the explicit comparison among \"finite layer objects\", \"$\\pm$-objec"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1804.00418","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"}