{"paper":{"title":"Large Shafarevich-Tate groups over quadratic number fields","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Myungjun Yu","submitted_at":"2018-01-31T16:42:59Z","abstract_excerpt":"Let $E$ be an elliptic curve over the rational field $\\mathbf{Q}$. Let $K$ be a quadratic extension over $\\mathbf{Q}$. Let $\\mathrm{ST}(E/K)$ dente the Shafarevich-Tate group of $E$ over $K$. We show that (under mild conditions on $E$) for every $r>0$, there are infinitely many quadratic twists $E^d/\\mathbf{Q}$ of $E/\\mathbf{Q}$ such that $\\mathrm{dim}_{\\mathbf{F}_2}(\\mathrm{ST}(E^d/K)[2]) > r$"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1801.10536","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"}