The rank of Jacobian varieties over the maximal abelian extensions of number fields: Towards the Frey-Jarden conjecture

Fumio Sairaiji; Takuya Yamauchi

doi:10.4153/CMB-2011-140-5

The rank of Jacobian varieties over the maximal abelian extensions of number fields: Towards the Frey-Jarden conjecture

Research output: Contribution to journal › Article › peer-review

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 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) = ∞ and for any abelian variety of GL₂-type with trivial character.

Original language	English
Pages (from-to)	842-849
Number of pages	8
Journal	Canadian Mathematical Bulletin
Volume	55
Issue number	4
DOIs	https://doi.org/10.4153/CMB-2011-140-5
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)

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10.4153/CMB-2011-140-5

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author = "Fumio Sairaiji and Takuya Yamauchi",

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AB - 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.

KW - Abelian points

KW - Frey-Jarden conjecture

KW - Jacobian varieties

KW - Mordell-Weil rank

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The rank of Jacobian varieties over the maximal abelian extensions of number fields: Towards the Frey-Jarden conjecture

Abstract

Keywords

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