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

Fumio Sairaiji, Takuya Yamauchi

Research output: Contribution to journalArticlepeer-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 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 languageEnglish
Pages (from-to)842-849
Number of pages8
JournalCanadian Mathematical Bulletin
Volume55
Issue number4
DOIs
Publication statusPublished - 2012 Dec
Externally publishedYes

Keywords

  • Abelian points
  • Frey-Jarden conjecture
  • Jacobian varieties
  • Mordell-Weil rank

ASJC Scopus subject areas

  • Mathematics(all)

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