{"paper":{"title":"Galois Module Structure of \\Z/\\ell^n-th Classes of Fields","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RT"],"primary_cat":"math.NT","authors_text":"Adam Topaz, Jan Minac, John Swallow","submitted_at":"2012-04-30T12:26:13Z","abstract_excerpt":"In this paper we use the Merkurjev-Suslin theorem to explore the structure of arithmetically significant Galois modules that arise from Kummer theory. Let K be a field of characteristic different from a prime \\ell, n a positive integer, and suppose that K contains the (\\ell^n)^th roots of unity. Let L be the maximal \\Z/\\ell^n-elementary abelian extension of K, and set G = \\Gal(L|K). We consider the G-module J = L^\\times/\\ell^n and denote its socle series by J_m. We provide a precise condition, in terms of a map to H^3(G,\\Z/\\ell^n), determining which submodules of J_{m-1} embed in cyclic module"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1204.6611","kind":"arxiv","version":4},"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"}