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Using class field theory, we shall show that our \\rho is an isomorphism of topological groups whose inverse is the Artin map of F. As a consequence of the construction of \\rho, we obtain an explicit description of F^ab. Fix a place \\infty of F, and let A be the subring of F consisting of those elements which are regular away from \\infty. We construct \\rho by combining th"},"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":"1110.3779","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2011-10-17T19:45:45Z","cross_cats_sorted":[],"title_canon_sha256":"7997ef9b87bda61cae0234931bf62185349dbb8c2c85d5f3613c8f2f9bbec731","abstract_canon_sha256":"86b6421dcd476000bc8017401e56353b72eca145328ef5e74ce25b5ed294423a"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:10:48.588365Z","signature_b64":"/iVnhJ1CGYM4h0MxDB8GLSCuKoAxLzPqHBDW+O4KUM0Pe6wOMmQFtk3IVcIg3L7+1CicOarh+Z5n4CiQmyj2BQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"358b8f074ba4ebfaf3e57a208f3e263b0222ad37d7aa8418960517a0ba798103","last_reissued_at":"2026-05-18T04:10:48.587907Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:10:48.587907Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Explicit Class Field Theory for global function fields","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"David Zywina","submitted_at":"2011-10-17T19:45:45Z","abstract_excerpt":"Let F be a global function field and let F^ab be its maximal abelian extension. 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