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On ranks of Jacobian varieties in prime degree extensions

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Mendes da Costa D.

Acta Arithmetica

2013

tom 161

nr 3

241-248

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.

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1 Acta Arithmetica

1 Mendes da Costa D.

1 2013

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On ranks of Jacobian varieties in prime degree extensions