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

2018/09/03 by Debargha Banerjee, Banerjee, Debargha, Narasimha Kumar +3
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #FOS: Mathematics #Finite Group Theory Research #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.1809.00456

openalex publication_date 2018/09/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this article, we prove a generalization of a theorem (Ogg's conjecture) due to Bary Mazur for arbitrary N∈ \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 \Ga₀(N) for any N ∈ \N. This in turn help us to determine the relevant part of the cuspidal subgroups without dependence on Shimura subgroups.

Related

• Ogg's conjectures over function fields
• Mazur's growth number conjecture and congruences
• Sylow-conjugate number fields
• Decay of weighted cusp counts for congruence subgroups of SL₂ over number fields
• The Unbounded Denominators Conjecture