The modularity of an abelian variety

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.

Publication Details

Journal
arXiv (Cornell University)
Published
2025-07-11
Primary Topic
Algebraic Geometry and Number Theory
Type
article
Field-Weighted Citation Impact
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article

The modularity of an abelian variety

arXiv (Cornell University)
Algebraic Geometry and Number Theory
article

The modularity of an abelian variety

article en

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.

arXiv (Cornell University)
Openalex Percentile: Top 44%
Algebraic Geometry and Number Theory
Open Access PDFOpenAlex
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The modularity of an abelian variety · arXiv (Cornell University) (2025) | TGRS Research Map | TGRS