On ranks of Jacobian varieties in prime degree extensions

• Autorzy: Dave Mendes da Costa
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 11G05: Elliptic curves over global fields

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Acta Arithmetica
• Rocznik: 2013
• Tom: 161
• Numer: 3
• Strony: 241-248

Daty

wydano

2013

Twórcy

autor

Dave Mendes da Costa

• School of Mathematics, University Walk, Bristol, BS8 1TW, United Kingdom

Identyfikatory

DOI

10.4064/aa161-3-3