On Serre's Conjecture over Imaginary Quadratic Fields

2011/06/28 by Rebecca Torrey, Torrey, Rebecca
Mathematics · #Algebraic Geometry and Number Theory #Analytic Number Theory Research #FOS: Mathematics #Mathematical Dynamics and Fractals #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.1106.5749

openalex publication_date 2011/06/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study an analog of Serre's conjecture over imaginary quadratic fields. In particular, we ask whether the weight recipe of Buzzard, Diamond and Jarvis will hold in this setting. Using a program written by the author, we provide computational evidence that this is in fact the case. In order to justify the method used in the program, we prove that a modular symbols method will work for arbitrary weights over imaginary quadratic fields.

Citations

• Modular Elliptic Curves and Fermat's Last Theorem

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