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We show that for each prime-to-$p$ number $n$ the $n$-torsion subgroup $\\H^2(F,\\mu_n)={}_n\\Br(F)$ is generated by $\\Z/n$-cyclic classes; in fact the $\\Z/n$-length is equal to two. It follows that the Brauer dimension of $F$ is two (first proved in \\cite{Sa97}), and any $F$-division algebra of period $n$ and index $n^2$ is decomposable."},"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":"1307.3345","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2013-07-12T06:39:26Z","cross_cats_sorted":["math.AG","math.NT"],"title_canon_sha256":"7b7ef8d180c8b21027fbb2f5a9626f1f884ed58cdbd2cebd31fd8ac93dfba806","abstract_canon_sha256":"55222829c4b55dc0623744ffdf5ebdc75ceb517d6ac885dfcd5e3a6292c15062"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:18:39.406018Z","signature_b64":"Qy7ruTV7q7hFPX4tvsWF/c9p6wj8HUglvu9AY8dEmn4LgGdeJYvB7cNESom0juGemcpoP2/JKcTnQdoJVqquCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9c1a6b3fc2a29e4e16955c83994440743870c42905bf2f84c77f7f8c9b2f5095","last_reissued_at":"2026-05-18T03:18:39.405546Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:18:39.405546Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Cyclic Length in the Tame Brauer Group of the Function Field of a p-Adic Curve","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG","math.NT"],"primary_cat":"math.RA","authors_text":"Eduardo Tengan, Eric Brussel, Kelly McKinnie","submitted_at":"2013-07-12T06:39:26Z","abstract_excerpt":"Let $F$ be the function field of a smooth curve over the $p$-adic number field $\\Q_p$. 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