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

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) = nBr(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 in [21]), and any F-division algebra of period n and index n2 is decomposable