{"paper":{"title":"On the Mordell-Weil ranks of supersingular abelian varieties in cyclotomic extensions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Antonio Lei, Gautier Ponsinet","submitted_at":"2018-07-19T18:51:34Z","abstract_excerpt":"Let $F$ be a number field unramified at an odd prime $p$ and $F_\\infty$ be the $\\mathbf{Z}_p$-cyclotomic extension of $F$. Let $A$ be an abelian variety defined over $F$ with good supersingular reduction at all primes of $F$ above $p$. B\\\"uy\\\"ukboduk and the first named author have defined modified Selmer groups associated to $A$ over $F_\\infty$. Assuming that the Pontryagin dual of these Selmer groups are torsion $\\mathbf{Z}_p[[\\mathrm{Gal}(F_\\infty/F)]]$-modules, we give an explicit sufficient condition for the rank of the Mordell-Weil group $A(F_n)$ to be bounded as $n$ varies."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1807.07604","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"}