The Mordell-Weil group of certain abelian varieties defined over the rational function field
type: Item
instance of: scholarly article
title: The Mordell-Weil group of certain abelian varieties defined over the rational function field
zbMATH Open document ID: 0759.14034
author: Fumio Hazama
published in: Tôhoku Mathematical Journal. Second Series
publication date: 1993-04-01T00:00:00Z
review text: An explicit method of construction of a family of abelian varieties each member of which has a large Mordell-Weil rank is given. For example, the following result is obtained: The elliptic curve \(E_ t:(t^ 6+2t^ 4+2t^ 2+1)y^ 2=x^ 3+2x^ 2+2x+1\) has Mordell-Weil rank \(\geq 2\) for every \(t\in\mathbb{Q}-\{0,\pm 1\}\). Further, an example of an elliptic curve defined over a function field of one variable is constructed such that its Mordell-Weil group is of arbitrarily high rank.
reviewed by: Fumio Hazama
Mathematics Subject Classification ID: 14K10
Mathematics Subject Classification ID: 14K15
Mathematics Subject Classification ID: 14G05
Mathematics Subject Classification ID: 14H52
zbMATH DE Number: 146176
zbMATH Keywords: family of abelian varieties
zbMATH Keywords: large Mordell-Weil rank
zbMATH Keywords: elliptic curve
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.2748/tmj/1178227300
OpenAlex ID: W2014158107
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DOI: 10.2748/TMJ/1178227300
description: scientific article; zbMATH DE number 146176