This is the second in a series of papers in which we study the n-Selmer group of an elliptic curve. In this paper, we show how to realize elements of the n-Selmer group explicitly as curves of degree n embedded in ℙn–1. The main tool we use is a comparison between an easily obtained embedding into ℙn2–1 and another map into ℙn2–1 that factors through the Segre embedding ℙn–1 × ℙn–1 → ℙn2–1. The comparison relies on an explicit version of the local-to-global principle for the n-torsion of the Brauer group of the base field.
© Walter de Gruyter Berlin · New York 2009