Explicit n-descent on elliptic curves, II. Geometry
Number Theory
2016-08-03 v1
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 P^{n-1}. The main tool we use is a comparison between an easily obtained embedding into P^{n^2-1} and another map into P^{n^2-1} that factors through the Segre embedding P^{n-1} x P^{n-1} --> P^{n^2-1}. 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.
Cite
@article{arxiv.math/0611606,
title = {Explicit n-descent on elliptic curves, II. Geometry},
author = {John Cremona and Tom Fisher and Cathy O'Neil and Denis Simon and Michael Stoll},
journal= {arXiv preprint arXiv:math/0611606},
year = {2016}
}
Comments
24 pages