Bounding the symbol length in the Galois cohomology of function fields of <var>p</var>-adic curves

Abstract

Let K be a function field of a p-adic curve and l a prime not equal to p. Assume that K contains a primitive l th root of unity. We show that every element in the l-torsion subgroup of the Brauer group of K is a tensor product of two cyclic algebras over K.