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ID 47192
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Author
Moon, Hyunsuk
Abstract
Let A be an abelian variety defined over a number field K. It is proved that for the composite field Kn of all Galois extensions over K of degree dividing n, the torsion subgroup of the Mordell-Weil group A(Kn) is finite. This is a variant of Ribet’s result ([7]) on the finiteness of torsion subgroup of A(K(ζ)). It is also proved that for the Jacobians of superelliptic curves yn = f(x) defined over K the Mordell-Weil group over the field generated by all nth roots of elements of K is the direct sum of a finite torsion group and a free ℤ-module of infinite rank.
Keywords
Mordell-Weil group
Jacobian
superelliptic curve
Published Date
2012-01
Publication Title
Mathematical Journal of Okayama University
Volume
volume54
Issue
issue1
Publisher
Department of Mathematics, Faculty of Science, Okayama University
Start Page
49
End Page
52
ISSN
0030-1566
NCID
AA00723502
Content Type
Journal Article
language
英語
Copyright Holders
Copyright©2012 by the Editorial Board of Mathematical Journal of Okayama University
File Version
publisher
Refereed
True
Submission Path
mjou/vol54/iss1/3
JaLCDOI