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 | |
| State | Published - Jan 1 2018 |
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All Science Journal Classification (ASJC) codes
- Mathematics(all)
- Applied Mathematics
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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 journal › Article
TY - JOUR
T1 - On Ribet’s isogeny for J0 (65)
AU - Klosin, Krzysztof
AU - Papikian, Mihran
PY - 2018/1/1
Y1 - 2018/1/1
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.
UR - http://www.scopus.com/inward/record.url?scp=85047667579&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=85047667579&partnerID=8YFLogxK
U2 - 10.1090/proc/14019
DO - 10.1090/proc/14019
M3 - Article
AN - SCOPUS:85047667579
VL - 146
SP - 3307
EP - 3320
JO - Proceedings of the American Mathematical Society
JF - Proceedings of the American Mathematical Society
SN - 0002-9939
IS - 8
ER -