On Ribet’s isogeny for J0 (65)

Krzysztof Klosin; Mihran Papikian

doi:10.1090/proc/14019

On Ribet’s isogeny for J₀ (65)

Krzysztof Klosin, Mihran Papikian

Mathematics

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

1 Scopus citations

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 language	English (US)
Pages (from-to)	3307-3320
Number of pages	14
Journal	Proceedings of the American Mathematical Society
Volume	146
Issue number	8
DOIs	https://doi.org/10.1090/proc/14019
State	Published - 2018

All Science Journal Classification (ASJC) codes

Mathematics(all)
Applied Mathematics

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title = "On Ribet{\textquoteright}s isogeny for J0 (65)",

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.",

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AU - Klosin, Krzysztof

AU - Papikian, Mihran

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N2 - 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.

AB - 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.

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