Journal
CANADIAN MATHEMATICAL BULLETIN-BULLETIN CANADIEN DE MATHEMATIQUES
Volume 55, Issue 4, Pages 842-849Publisher
CANADIAN MATHEMATICAL SOC
DOI: 10.4153/CMB-2011-140-5
Keywords
Mordell-Weil rank; Jacobian varieties; Frey-Jarden conjecture; abelian points
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Funding
- JSPS [18005, 18740021, 19740017]
- Grants-in-Aid for Scientific Research [22340001, 19740017, 18740021] Funding Source: KAKEN
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Frey and Jarden asked if any abelian variety over a number field K has the infinite Mordell-Weil rank over the maximal abelian extension K-ab. In this paper, we give an affirmative answer to their conjecture for the Jacobian variety of any smooth projective curve C over K such that #C(K-ab) = infinity and for any abelian variety of GL(2)-type with trivial character.
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