On Ribet’s isogeny for J0 (65)

Krzysztof Klosin, Mihran Papikian

Research output: Contribution to journalArticle

Abstract

Let J65 be the Jacobian of the Shimura curve attached to the indefinite quaternion algebra over ℚ of discriminant 65. We study the isogenies J0 (65) → J65 defined over ℚ, whose existence was proved by Ribet. We prove that there is an isogeny whose kernel is supported on the Eisenstein maximal ideals of the Hecke algebra acting on J0 (65), and, moreover, the odd part of the kernel is generated by a cuspidal divisor of order 7, as is predicted by a conjecture of Ogg.

Original languageEnglish (US)
Pages (from-to)3307-3320
Number of pages14
JournalProceedings of the American Mathematical Society
Volume146
Issue number8
DOIs
StatePublished - Jan 1 2018

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Isogeny
Algebra
Isogenies
kernel
Quaternion Algebra
Hecke Algebra
Maximal Ideal
Discriminant
Divisor
Odd
Curve

All Science Journal Classification (ASJC) codes

  • Mathematics(all)
  • Applied Mathematics

Cite this

Klosin, Krzysztof ; Papikian, Mihran. / On Ribet’s isogeny for J0 (65). In: Proceedings of the American Mathematical Society. 2018 ; Vol. 146, No. 8. pp. 3307-3320.
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On Ribet’s isogeny for J0 (65). / Klosin, Krzysztof; Papikian, Mihran.

In: Proceedings of the American Mathematical Society, Vol. 146, No. 8, 01.01.2018, p. 3307-3320.

Research output: Contribution to journalArticle

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