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Explicit n-descent on elliptic curves, II. Geometry
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J. E. Cremona
Published/Copyright:
June 16, 2009
Abstract
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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- Explicit n-descent on elliptic curves, II. Geometry
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Articles in the same Issue
- Ends of locally symmetric spaces with maximal bottom spectrum
- Subsystems of finite type and semigroup invariants of subshifts
- Explicit n-descent on elliptic curves, II. Geometry
- On function fields with free absolute Galois groups
- Ternary cyclotomic polynomials having a large coefficient
- The Minus Conjecture revisited
- On the moduli space of certain smooth codimension-one foliations of the 5-sphere by complex surfaces
- Arithmetic duality theorems for 1-motives over function fields
- Arithmetic duality theorems for 1-motives
