The modularity of an abelian variety
Number Theory
2026-01-30 v2 Algebraic Geometry
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.
Keywords
Cite
@article{arxiv.2507.08970,
title = {The modularity of an abelian variety},
author = {Jae-Hyun Yang},
journal= {arXiv preprint arXiv:2507.08970},
year = {2026}
}
Comments
20 pages. arXiv admin note: text overlap with arXiv:0706.4268