Cyclic Length in the Tame Brauer Group of the Function Field of a p-Adic Curve

2013/07/12 by Eric Brussel, Brussel, Eric, Kelly McKinnie +3
Mathematics · #11G20 #11R58 #14E22 #16K50 #Algebraic Geometry (math.AG) #FOS: Mathematics #Number Theory (math.NT) #Rings and Algebras (math.RA) #math.AG #math.NT #math.RA #msc:11G20 #msc:11R58 #msc:14E22 #msc:16K50

paper · pdf · doi:10.48550/arxiv.1307.3345

arxiv created 2013/07/12 · arxiv updated 2013/07/15

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 two (first proved in \citeSa97), and any F-division algebra of period n and index n² is decomposable.

Related

• Cyclicity and indecomposability in the Brauer group of a p-adic curve
• Tame division algebras of prime period over function fields of p-adic curves
• Cyclic Algebras over p-adic curves
• Generalized period-index problem with an application to quadratic forms
• Division Algebra Cyclicity in Prime Degree over a p-Adic Curve