On the Mordell-Weil group of certain abelian varieties defined over the rational function field
type: Item
instance of: scholarly article
title: On the Mordell-Weil group of certain abelian varieties defined over the rational function field
zbMATH Open document ID: 0729.14019
DOI: 10.1016/S0022-314X(05)80034-4
author: Fumio Hazama
published in: Journal of Number Theory
publication date: 1991-01-01T00:00:00Z
review text: The aim of this paper is to prove the following theorem, which generalizes a recent result of \textit{C. Wajngurt} [J. Number Theory 23, 80-85 (1986; Zbl 0584.14019)]: Let C be a hyperelliptic curve over a field k, and let A be an abelian variety over k. Denote by \(A_ b\) the twist of A defined by the quadratic extension \(k(C)/k({\mathbb{P}}^ 1)\). Then we have an isomorphism of abelian groups \(A_ b(k(t))\cong Hom_ K(J(C),A)\oplus A_ 2(k),\) where \(A_ 2(k)\) denotes the group of k- rational 2-division points of A.
Mathematics Subject Classification ID: 14G05
Mathematics Subject Classification ID: 14K15
Mathematics Subject Classification ID: 14H52
Mathematics Subject Classification ID: 14H40
Mathematics Subject Classification ID: 14K22
zbMATH DE Number: 4204539
zbMATH Keywords: rational points
zbMATH Keywords: Jacobian
zbMATH Keywords: hyperelliptic curve
reviewed by: Lucian Bădescu
MaRDI profile type: Publication
cites work: Théoremes de finitude en cohomologie galoisienne
cites work: Q3663443
cites work: Q3849064
cites work: Rational solutions of Diophantine equations isomorphic to elliptic curves with applications to complex multiplication
full work available at URL: s0022-314x(05)80034-4
OpenAlex ID: W1990015571
description: scientific article; zbMATH DE number 4204539