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

Eric Brussel; Kelly McKinnie; Eduardo Tengan

doi:10.1353/ajm.2016.0020

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

Eric Brussel, Kelly McKinnie, Eduardo Tengan

Mathematics

Research output: Contribution to journal › Article › peer-review

4 Scopus citations

Abstract

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 H²(F,μ_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 three (first proved by Saltman), and any F-division algebra of period n and index n² is decomposable.

Original language	English
Pages (from-to)	251-286
Number of pages	36
Journal	American Journal of Mathematics
Volume	138
Issue number	2
DOIs	https://doi.org/10.1353/ajm.2016.0020
State	Published - Apr 2016

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10.1353/ajm.2016.0020

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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.",

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AB - 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.

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

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