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December 2014 Eisenstein Ideals and the Rational Torsion Subgroups of Modular Jacobian Varieties II
Masami OHTA
Tokyo J. Math. 37(2): 273-318 (December 2014). DOI: 10.3836/tjm/1422452795

Abstract

We study the rational torsion subgroup of the modular Jacobian variety $J_0(N)$ when $N$ is square-free. We prove that the $p$-primary part of this group coincides with that of the cuspidal divisor class group for $p\geq 3$ when $3 \nmid N$, and for $p\geq 5$ when $3 \mid N$. We further determine the structure of each eigenspace of such $p$-primary part with respect to the Atkin-Lehner involutions. This is based on our study of the Eisenstein ideals in the Hecke algebras.

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Masami OHTA. "Eisenstein Ideals and the Rational Torsion Subgroups of Modular Jacobian Varieties II." Tokyo J. Math. 37 (2) 273 - 318, December 2014. https://doi.org/10.3836/tjm/1422452795

Information

Published: December 2014
First available in Project Euclid: 28 January 2015

zbMATH: 1332.11061
MathSciNet: MR3304683
Digital Object Identifier: 10.3836/tjm/1422452795

Rights: Copyright © 2014 Publication Committee for the Tokyo Journal of Mathematics

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Vol.37 • No. 2 • December 2014
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