A generalization of Mazur's theorem (Ogg's conjecture) for number fields

Abstract

In this article, we prove a generalization of a theorem (Ogg's conjecture) due to Bary Mazur for arbitrary $N\in \mathbb{N}$ and for {\it number fields}. The main new observation is a modification of a theorem due to Glenn Stevens for the congruence subgroups of the form $\Ga_0(N)$ for any $N\in \mathbb{N}$. This in turn help us to determine the relevant part of the cuspidal subgroups without dependence on Shimura subgroups.

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