{"paper":{"title":"Selmer groups over $\\Z_p^d$-extensions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Ki-Seng Tan","submitted_at":"2012-05-17T11:23:59Z","abstract_excerpt":"Consider an abelian variety $A$ defined over a global field $K$ and let $L/K$ be a $\\Z_p^d$-extension, unramified outside a finite set of places of $K$, with $\\Gal(L/K)=\\Gamma$. Let $\\Lambda(\\Gamma):=\\Z_p[[\\Gamma]]$ denote the Iwasawa algebra. In this paper, we study how the characteristic ideal of the $\\Lambda(\\Gamma)$-module $X_L$, the dual $p$-primary Selmer group, varies when $L/K$ is replaced by a intermediate $\\Z_p^e$-extension."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1205.3907","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"}