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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 ISSN 0075-4102.
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Official URL: http://dx.doi.org/10.1515/CRELLE.2009.050
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, Engineering and Medicine > 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: |
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| 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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