Cyclic Algebras over p-adic curves
Saltman, David J.
Original · EN
In this paper we study division algebras over the function fields of curves over ₚ. 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 ₚ. 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 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.
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