On ranks of Jacobian varieties in prime degree extensions

Dave Mendes da Costa. "On ranks of Jacobian varieties in prime degree extensions." Acta Arithmetica 161.3 (2013): 241-248. <http://eudml.org/doc/279767>.

@article{DaveMendesdaCosta2013,
abstract = {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.},
author = {Dave Mendes da Costa},
journal = {Acta Arithmetica},
keywords = {Jacobian variety; elliptic curve; number field; rank; Goldfeld's conjecture; projective curve},
language = {eng},
number = {3},
pages = {241-248},
title = {On ranks of Jacobian varieties in prime degree extensions},
url = {http://eudml.org/doc/279767},
volume = {161},
year = {2013},
}

TY - JOUR
AU - Dave Mendes da Costa
TI - On ranks of Jacobian varieties in prime degree extensions
JO - Acta Arithmetica
PY - 2013
VL - 161
IS - 3
SP - 241
EP - 248
AB - 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.
LA - eng
KW - Jacobian variety; elliptic curve; number field; rank; Goldfeld's conjecture; projective curve
UR - http://eudml.org/doc/279767
ER -