The modularity of an abelian variety

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 comment20 pages. arXiv admin note: text overlap with arXiv:0706.4268