2024/08/27 by Mohamed Moakher, Moakher, Mohamed
Mathematics · #11G10 #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #Analytic Number Theory Research #FOS: Mathematics #Number Theory (math.NT) #Primary 11F33 #Secondary 11F80
paper · pdf · doi:10.48550/arxiv.2408.15410
openalex publication_date 2024/08/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We generalize a result of Ribet and Takahashi on the parametrization of elliptic curves by Shimura curves to the Hilbert modular setting. In particular, we study the behaviour of the parametrization of modular abelian varieties by Shimura curves associated to quaternion algebras D over a totally real field F, as we vary D. As a consequence, we obtain that on these Shimura curves, the cohomological congruence module is equal to the ring theoretic congruence module even in cases where we do not have multiplicity one, thereby extending results of Manning and Böckle-Khare-Manning.