Cyclic length in the tame brauer group of the function field of a p-ADIC curve

Eric Brussel, Kelly McKinnie, Eduardo Tengan

Research output: Contribution to journalArticlepeer-review

Abstract

Let F be the function field of a smooth curve over the p-adic number field Qp. We show that for each prime-to-p number n the n-torsion subgroup H2(F,μn)=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 three (first proved by Saltman), and any F-division algebra of period n and index n2 is decomposable.

Original languageEnglish
Pages (from-to)251-286
Number of pages36
JournalAmerican Journal of Mathematics
Volume138
Issue number2
DOIs
StatePublished - Apr 2016

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