Geodesic
The Rank of Jacobian Varieties over the Maximal Abelian Extensions of Number Fields: Towards the Frey–Jarden Conjecture
Canadian mathematical bulletin, Tome 55 (2012) no. 4, pp. 842-849

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DOI

Frey and Jarden asked if any abelian variety over a number field $K$ has the infinite Mordell–Weil rank over the maximal abelian extension ${{K}^{\text{ab}}}$ . 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 $\sharp C\left( {{K}^{\text{ab}}} \right)\,=\,\infty $ and for any abelian variety of $\text{G}{{\text{L}}_{2}}$ -type with trivial character.
DOI : 10.4153/CMB-2011-140-5
Mots-clés : 11G05, 11D25, 14G25, 14K07, Mordell–Weil rank, Jacobian varieties, Frey-Jarden conjecture, abelian points 
Sairaiji, Fumio; Yamauchi, Takuya. The Rank of Jacobian Varieties over the Maximal Abelian Extensions of Number Fields: Towards the Frey–Jarden Conjecture. Canadian mathematical bulletin, Tome 55 (2012) no. 4, pp. 842-849. doi: 10.4153/CMB-2011-140-5
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     title = {The {Rank} of {Jacobian} {Varieties} over the {Maximal} {Abelian} {Extensions} of {Number} {Fields:} {Towards} the {Frey{\textendash}Jarden} {Conjecture}},
     journal = {Canadian mathematical bulletin},
     pages = {842--849},
     year = {2012},
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     doi = {10.4153/CMB-2011-140-5},
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