{"paper":{"title":"Pontryagin duality for Iwasawa modules and abelian varieties","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Fabien Trihan, Ignazio Longhi, King Fai Lai, Ki-Seng Tan","submitted_at":"2014-06-23T06:33:08Z","abstract_excerpt":"We prove a functional equation for two projective systems of finite abelian $p$-groups, $\\{\\fa_n\\}$ and $\\{\\fb_n\\}$, endowed with an action of $\\ZZ_p^d$ such that $\\fa_n$ can be identified with the Pontryagin dual of $\\fb_n$ for all $n$.\n  Let $K$ be a global field. Let $L$ be a $\\ZZ_p^d$-extension of $K$ ($d\\geq 1$), unramified outside a finite set of places. Let $A$ be an abelian variety over $K$. We prove an algebraic functional equation for the Pontryagin dual of the Selmer group of $A$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1406.5815","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"}