{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:VEYS3VNB6XDKO74JK7XGPEJN33","short_pith_number":"pith:VEYS3VNB","schema_version":"1.0","canonical_sha256":"a9312dd5a1f5c6a77f8957ee67912ddedebdd73d09d86d6f201872230c1c051e","source":{"kind":"arxiv","id":"1204.6611","version":4},"attestation_state":"computed","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"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1204.6611","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2012-04-30T12:26:13Z","cross_cats_sorted":["math.RT"],"title_canon_sha256":"a4232a96b2870e9ac592829ae8ae43e88e5c1e9066abe28552fb0e1522ba2285","abstract_canon_sha256":"c10d9a7b3ac868dd466e6f7ca81c21f523edd4adc94702a458350a4af96c2dd8"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:23:35.826029Z","signature_b64":"Yt9R68rN64wp5ksjqeqVLOGG+t6ZXcgLCm1fhYK4XvTvqSh50dqyGlg6WmRcjQKQQL0yQONn5arlZKE8sPC9Cg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a9312dd5a1f5c6a77f8957ee67912ddedebdd73d09d86d6f201872230c1c051e","last_reissued_at":"2026-05-18T02:23:35.825327Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:23:35.825327Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1204.6611","created_at":"2026-05-18T02:23:35.825460+00:00"},{"alias_kind":"arxiv_version","alias_value":"1204.6611v4","created_at":"2026-05-18T02:23:35.825460+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1204.6611","created_at":"2026-05-18T02:23:35.825460+00:00"},{"alias_kind":"pith_short_12","alias_value":"VEYS3VNB6XDK","created_at":"2026-05-18T12:27:25.539911+00:00"},{"alias_kind":"pith_short_16","alias_value":"VEYS3VNB6XDKO74J","created_at":"2026-05-18T12:27:25.539911+00:00"},{"alias_kind":"pith_short_8","alias_value":"VEYS3VNB","created_at":"2026-05-18T12:27:25.539911+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/VEYS3VNB6XDKO74JK7XGPEJN33","json":"https://pith.science/pith/VEYS3VNB6XDKO74JK7XGPEJN33.json","graph_json":"https://pith.science/api/pith-number/VEYS3VNB6XDKO74JK7XGPEJN33/graph.json","events_json":"https://pith.science/api/pith-number/VEYS3VNB6XDKO74JK7XGPEJN33/events.json","paper":"https://pith.science/paper/VEYS3VNB"},"agent_actions":{"view_html":"https://pith.science/pith/VEYS3VNB6XDKO74JK7XGPEJN33","download_json":"https://pith.science/pith/VEYS3VNB6XDKO74JK7XGPEJN33.json","view_paper":"https://pith.science/paper/VEYS3VNB","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1204.6611&json=true","fetch_graph":"https://pith.science/api/pith-number/VEYS3VNB6XDKO74JK7XGPEJN33/graph.json","fetch_events":"https://pith.science/api/pith-number/VEYS3VNB6XDKO74JK7XGPEJN33/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/VEYS3VNB6XDKO74JK7XGPEJN33/action/timestamp_anchor","attest_storage":"https://pith.science/pith/VEYS3VNB6XDKO74JK7XGPEJN33/action/storage_attestation","attest_author":"https://pith.science/pith/VEYS3VNB6XDKO74JK7XGPEJN33/action/author_attestation","sign_citation":"https://pith.science/pith/VEYS3VNB6XDKO74JK7XGPEJN33/action/citation_signature","submit_replication":"https://pith.science/pith/VEYS3VNB6XDKO74JK7XGPEJN33/action/replication_record"}},"created_at":"2026-05-18T02:23:35.825460+00:00","updated_at":"2026-05-18T02:23:35.825460+00:00"}