Cyclic Algebras over p-adic curves

2006/04/18 by David J. Saltman, Saltman, David J. · 1 citation
Mathematics · #Algebraic Geometry (math.AG) #FOS: Mathematics #Rings and Algebras (math.RA) #math.AG #math.RA

paper · pdf · doi:10.48550/arxiv.math/0604409

arxiv created 2006/04/18 · arxiv updated 2009/12/01

Abstract

In this paper we study division algebras over the function fields of curves over \Q_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 \Z_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 \not= 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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