Jump to ContentJump to Main Navigation
Show Summary Details
More options …

Journal für die reine und angewandte Mathematik

Managing Editor: Weissauer, Rainer

Ed. by Colding, Tobias / Huybrechts, Daniel / Hwang, Jun-Muk / Williamson, Geordie


IMPACT FACTOR 2018: 1.859

CiteScore 2018: 1.14

SCImago Journal Rank (SJR) 2018: 2.554
Source Normalized Impact per Paper (SNIP) 2018: 1.411

Mathematical Citation Quotient (MCQ) 2018: 1.55

Online
ISSN
1435-5345
See all formats and pricing
More options …
Volume 2009, Issue 632

Issues

Explicit n-descent on elliptic curves, II. Geometry

J. E. Cremona
  • Mathematics Institute, Zeeman Building, University of Warwick, Coventry CV4 7AL, UK. e-mail:
  • Other articles by this author:
  • De Gruyter OnlineGoogle Scholar
/ T. A. Fisher
  • University of Cambridge, DPMMS, Centre for Mathematical Sciences, Wilberforce Road, Cambridge CB3 0WB, UK. e-mail:
  • Other articles by this author:
  • De Gruyter OnlineGoogle Scholar
/ C. O'Neil
  • Barnard College, Columbia University, Department of Mathematics, 2990 Broadway MC 4418, New York, NY 10027-6902, USA. e-mail:
  • Other articles by this author:
  • De Gruyter OnlineGoogle Scholar
/ D. Simon
  • Université de Caen, Campus II—Boulevard Maréchal Juin, BP 5186, 14032 Caen, France. e-mail:
  • Other articles by this author:
  • De Gruyter OnlineGoogle Scholar
/ M. Stoll
Published Online: 2009-06-16 | DOI: https://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 × 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.

About the article

Received: 2006-12-14

Revised: 2008-02-14

Published Online: 2009-06-16

Published in Print: 2009-07-01


Citation Information: Journal für die reine und angewandte Mathematik (Crelles Journal), Volume 2009, Issue 632, Pages 63–84, ISSN (Online) 1435-5345, ISSN (Print) 0075-4102, DOI: https://doi.org/10.1515/CRELLE.2009.050.

Export Citation

Citing Articles

Here you can find all Crossref-listed publications in which this article is cited. If you would like to receive automatic email messages as soon as this article is cited in other publications, simply activate the “Citation Alert” on the top of this page.

[1]
Gábor Ivanyos, Péter Kutas, and Lajos Rónyai
Foundations of Computational Mathematics, 2017
[2]
Tom Fisher
The Open Book Series, 2013, Volume 1, Number 1, Page 395
[3]
John E. Cremona, Tom A. Fisher, and Michael Stoll
Algebra & Number Theory, 2010, Volume 4, Number 6, Page 763

Comments (0)

Please log in or register to comment.
Log in