A genus one curve defined over $\mathbb{Q}$ which has points over $\mathbb{Q}_{p}$ for all primes $p$ may not have a rational point. It is natural to study the classes of $\mathbb{Q}$ -extensions over which all such curves obtain a global point. In this article, we show that every such genus one curve with semistable Jacobian has a point defined over a solvable extension of $\mathbb{Q}$
Publié le : 2008-04-15
Classification:
14G05,
14H45,
14H52,
11R34,
11R23
@article{1208958385,
author = {\c Ciperiani, Mirela and Wiles, Andrew},
title = {Solvable points on genus one curves},
journal = {Duke Math. J.},
volume = {141},
number = {1},
year = {2008},
pages = { 381-464},
language = {en},
url = {http://dml.mathdoc.fr/item/1208958385}
}
Çiperiani, Mirela; Wiles, Andrew. Solvable points on genus one curves. Duke Math. J., Tome 141 (2008) no. 1, pp. 381-464. http://gdmltest.u-ga.fr/item/1208958385/