Cyclic length in the Brauer group of a p-adic elliptic curve

Abstract

Let K be a finite extension of , and E be an elliptic curve over K with good ordinary reduction. We study the cyclic length of the p-primary part of the Brauer group of E. In particular, for , we show that all elements in the p-torsion of are p-cyclic whenever p divides the number of -points of the reduction of E modulo p.