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Licensed Unlicensed Requires Authentication Published by De Gruyter June 16, 2009

Explicit n-descent on elliptic curves, II. Geometry

  • J. E. Cremona , T. A. Fisher , C. O'Neil , D. Simon and M. Stoll


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.

Received: 2006-12-14
Revised: 2008-02-14
Published Online: 2009-06-16
Published in Print: 2009-July

© Walter de Gruyter Berlin · New York 2009

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