English

The Tate Conjecture for Certain Abelian Varieties over Finite Fields

Number Theory 2021-01-27 v1 Algebraic Geometry

Abstract

Tate's theorem (Invent. Math. 1966)implies that the Tate conjecture holds for any abelian variety over a finite field whose Q_l-algebra of Tate classes is generated by those of degree 1. We construct families of abelian varieties over finite fields for which this condition fails, but for which we are nevertheless able to prove the Tate conjecture.

Keywords

Cite

@article{arxiv.math/9911218,
  title  = {The Tate Conjecture for Certain Abelian Varieties over Finite Fields},
  author = {J. S. Milne},
  journal= {arXiv preprint arXiv:math/9911218},
  year   = {2021}
}

Comments

28 pages

R2 v1 2026-07-22T18:05:26.594Z