{"paper":{"title":"Control Theorems for l-adic Lie extensions of global function fields","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Andrea Bandini, Maria Valentino","submitted_at":"2012-06-13T11:02:48Z","abstract_excerpt":"Let F be a global function field of characteristic p>0, K/F an l-adic Lie extension unramified outside a finite set of places S and A/F an abelian variety without complex multiplication. We study Sel_A(K)_l^\\vee (the Pontrjagin dual of the Selmer group) and (under some mild hypotheses) prove that it is a finitely generated Z_l[[\\Gal(K/F)]]-module via generalizations of Mazur's Control Theorem. If Gal(K/F) has no elements of order l and contains a closed normal subgroup H such that Gal(K/F)/H\\simeq Z_l, we are able to give sufficient conditions for Sel_A(K)_l^\\vee to be finitely generated as Z_"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1206.2767","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"}