Abstract
Frey and Jarden asked if any abelian variety over a number field K has the infinite Mordell- Weil rank over the maximal abelian extension Kab. 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) = ∞ and for any abelian variety of GL2-type with trivial character.
Original language | English |
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Pages (from-to) | 842-849 |
Number of pages | 8 |
Journal | Canadian Mathematical Bulletin |
Volume | 55 |
Issue number | 4 |
DOIs | |
Publication status | Published - 2012 Dec |
Externally published | Yes |
Keywords
- Abelian points
- Frey-Jarden conjecture
- Jacobian varieties
- Mordell-Weil rank
ASJC Scopus subject areas
- Mathematics(all)