The modularity of an abelian variety

2025/07/11 by Yang, Jae-Hyun
#11F46 #11F80 #14G35 #14Kxx #Algebraic Geometry (math.AG) #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2507.08970

Abstract

We introduce the concept of the modularity of an abelian variety defined over the rational number field extending the modularity of an elliptic curve. We discuss the modularity of an abelian variety over the rational number field. We conjecture that a simple abelian variety over the rational number field is modular.

Citations

• Modular Elliptic Curves and Fermat's Last Theorem
• Galois representations associated to Siegel modular forms of low weight

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