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Explicit n-descent on elliptic curves, II. Geometry

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Cremona, J. E., Fisher, T. A., O'Neil, C., Simon, D. and Stoll, M. (2009) Explicit n-descent on elliptic curves, II. Geometry. Journal fur die reine und angewandte Mathematik, Volume 2009 (Number 632). pp. 63-84. doi:10.1515/CRELLE.2009.050

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Official URL: http://dx.doi.org/10.1515/CRELLE.2009.050

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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 x 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.

Item Type: Journal Article
Subjects: Q Science > QA Mathematics
Divisions: Faculty of Science > Mathematics
Journal or Publication Title: Journal fur die reine und angewandte Mathematik
Publisher: Walter de Gruyter & Co
ISSN: 0075-4102
Official Date: July 2009
Dates:
DateEvent
July 2009Published
Volume: Volume 2009
Number: Number 632
Number of Pages: 22
Page Range: pp. 63-84
DOI: 10.1515/CRELLE.2009.050
Status: Peer Reviewed
Publication Status: Published
Access rights to Published version: Restricted or Subscription Access

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