A note on the growth of Mordell-Weil ranks of elliptic curves in cyclotomic $\mathbf {Z}_p$-extensions

A note on the growth of Mordell-Weil ranks of elliptic curves in cyclotomic $\mathbf {Z}_p$-extensions

Kazuo Matsuno

Source: Proc. Japan Acad. Ser. A Math. Sci. Volume 79, Number 5 (2003), 101-104.

Abstract

In this note, we exhibit some examples of elliptic curves whose Mordell-Weil ranks grow in lower layer of the cyclotomic $\mathbf{Z}_p$-extension over the rationals.

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Primary Subjects: 11G05, 11R23

Keywords: Elliptic curve; Mordell-Weil group; Iwasawa theory; $\mathbf {Z}_p$-extension

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Links and Identifiers

Permanent link to this document: http://projecteuclid.org/euclid.pja/1116443678
Mathematical Reviews number (MathSciNet): MR1980609
Zentralblatt MATH identifier: 02052922
Digital Object Identifier: doi:10.3792/pjaa.79.101

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