Geodesic
On ranks of Jacobian varieties in prime degree extensions
Dave Mendes da Costa1
1 School of Mathematics University Walk Bristol, BS8 1TW, United Kingdom
Acta Arithmetica, Tome 161 (2013) no. 3, pp. 241-248.

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

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.
DOI : 10.4064/aa161-3-3
Keywords: dokchitser acta arith showed given elliptic curve defined number field there infinitely many degree extensions which rank larger present paper replace prime number result follows general result establishing similar property jacobian varieties associated curves defined equation shape where polynomials coprime degree

Dave Mendes da Costa 1

1 School of Mathematics University Walk Bristol, BS8 1TW, United Kingdom 
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Dave Mendes da Costa. On ranks of Jacobian varieties in prime degree extensions. Acta Arithmetica, Tome 161 (2013) no. 3, pp. 241-248. doi : 10.4064/aa161-3-3. http://geodesic.mathdoc.fr/articles/10.4064/aa161-3-3/

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