Indecomposability and cyclicity in the p-primary part of the Brauer group of a p-adic curve

Abstract

We obtain two results about the p-primary part of the Brauer group of a p-adic curve X. First, assuming enough roots of unity and that X has good reduction, we construct indecomposable K(X)-division algebras of period p2 and index p3. Second, for an elliptic curve X with split multiplicative reduction, we show that all order p elements of are -cyclic, and that if moreover X is defined over that all order pr elements of are -cyclic for