{"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 $\\Q_p$. 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."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1307.3345","kind":"arxiv","version":1},"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"}