T. Dokchitser [Acta Arith. 126 (2007)] showed that given an elliptic curve E defined over a number field K then there are infinitely many degree 3 extensions L/K for which the rank of E(L) is larger than E(K). In the present paper we show that the same is true if we replace 3 by any prime number. This result follows from a more general result establishing a similar property for the Jacobian varieties associated with curves defined by an equation of the shape f(y) = g(x) where f and g are polynomials of coprime degree.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-aa161-3-3,
author = {Dave Mendes da Costa},
title = {On ranks of Jacobian varieties in prime degree extensions},
journal = {Acta Arithmetica},
volume = {161},
year = {2013},
pages = {241-248},
zbl = {1291.11093},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-aa161-3-3}
}
Dave Mendes da Costa. On ranks of Jacobian varieties in prime degree extensions. Acta Arithmetica, Tome 161 (2013) pp. 241-248. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-aa161-3-3/