Ribet's conjecture for Eisenstein maximal ideals
Number Theory
2022-02-07 v2
Abstract
According to Ogg's conjecture (Mazur's Theorem), cuspidal subgroup coincides with rational torsion points of the Jacobian variety of modular curves of the form for a {\it prime} number . There is a recent interest to generalize the conjecture for arbitrary by Ribet, Ohta and Yoo. In this direction, Ribet conjectured that all the Eisenstein maximal ideals are "cuspidal". Hwajong Yoo proved the conjecture ( under certain hypothesis) provided that those ideals are {\it rational}. In this article, we show that ( under certain hypothesis), Ribet's conjecture is true for {\it non-rational} Eisenstein maximal ideals.
Keywords
Cite
@article{arxiv.2111.07747,
title = {Ribet's conjecture for Eisenstein maximal ideals},
author = {Debargha Banerjee and Narasimha Kumar and Dipramit Majumdar},
journal= {arXiv preprint arXiv:2111.07747},
year = {2022}
}