Solvable points on genus one curves
Andrew Wiles and Mirela Çiperiani
Source: Duke Math. J. Volume 142, Number 3 (2008), 381-464.
Abstract
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 $\mathbb{Q}$
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Permanent link to this document: http://projecteuclid.org/euclid.dmj/1208958385
Digital Object Identifier: doi:10.1215/00127094-2008-010
Duke Mathematical Journal