CYCLIC LENGTH IN THE TAME BRAUER GROUP OF THE FUNCTION FIELD OF A p-ADIC CURVE

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 H-2 (F, mu(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 n(2) is decomposable.