{"paper":{"title":"Algebraic functional equations and completely faithful Selmer groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Gergely Z\\'abr\\'adi, Tibor Backhausz","submitted_at":"2014-05-23T19:00:15Z","abstract_excerpt":"Let $E$ be an elliptic curve---defined over a number field $K$---without complex multiplication and with good ordinary reduction at all the primes above a rational prime $p \\geq 5$. We construct a pairing on the dual $p^\\infty$-Selmer group of $E$ over any strongly admissible $p$-adic Lie extension $K_\\infty/K$ under the assumption that it is a torsion module over the Iwasawa algebra of the Galois group $G=\\operatorname{Gal}(K_\\infty/K)$. Under some mild additional hypotheses this gives an algebraic functional equation of the conjectured $p$-adic L-function. As an application we construct comp"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1405.6180","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"}