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.
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Venapally Suresh, Bounding the symbol length in the Galois cohomology of function fields of <var>p</var>-adic curves. Comment. Math. Helv. 85 (2010), no. 2, pp. 337–346DOI 10.4171/CMH/198