{"paper":{"title":"Ranks of GL2 Iwasawa modules of elliptic curves","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Tibor Backhausz","submitted_at":"2013-03-04T14:35:10Z","abstract_excerpt":"Let $p >= 5$ be a prime and $E$ an elliptic curve without complex multiplication and let $K_\\infty=Q(E[p^\\infty])$ be a pro-$p$ Galois extension over a number field $K$. We consider $X(E/K_\\infty)$, the Pontryagin dual of the $p$-Selmer group $\\Sel_{p^\\infty}(E/K_\\infty)$. The size of this module is roughly measured by its rank $\\tau$ over a $p$-adic Galois group algebra $\\Lambda(H)$, which has been studied in the past decade. We prove $\\tau >= 2$ for almost every elliptic curve under standard assumptions. Following from a result of Coates et al, $\\tau$ is odd if and only if $[Q(E[p]) \\colon Q"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1303.0710","kind":"arxiv","version":4},"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"}