Open Access
July, 2013 Eisenstein ideals and the rational torsion subgroups of modular Jacobian varieties
Masami OHTA
J. Math. Soc. Japan 65(3): 733-772 (July, 2013). DOI: 10.2969/jmsj/06530733


Let $N \geq 5$ be a prime number. Conrad, Edixhoven and Stein have conjectured that the rational torsion subgroup of the modular Jacobian variety $J_1(N)$ coincides with the 0-cuspidal class group. We prove this conjecture up to 2-torsion. To do this, we study certain ideals of the Hecke algebras, called the Eisenstein ideals, related to modular forms of weight 2 with respect to $\varGamma_1(N)$ that vanish at the 0-cusps.


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Masami OHTA. "Eisenstein ideals and the rational torsion subgroups of modular Jacobian varieties." J. Math. Soc. Japan 65 (3) 733 - 772, July, 2013.


Published: July, 2013
First available in Project Euclid: 23 July 2013

zbMATH: 1318.11081
MathSciNet: MR3084978
Digital Object Identifier: 10.2969/jmsj/06530733

Primary: 11G18 , 14G35
Secondary: 11F11 , 14G05

Keywords: Eisenstein ideal , modular Jacobian variety , rational torsion subgroup

Rights: Copyright © 2013 Mathematical Society of Japan

Vol.65 • No. 3 • July, 2013
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