Cyclic algebras over p-adic curves

AbstractIn this paper we study division algebras over the function fields of curves over Qp. The first and main tool is to view these fields as function fields over nonsingular S which are projective of relative dimension 1 over the p adic ring Zp. A previous paper showed such division algebras had index bounded by n2 assuming the exponent was n and n was prime to p. In this paper we consider algebras of prime degree (and hence exponent) q≠p and show these algebras are cyclic. We also find a geometric criterion for a Brauer class to have index q