The Tate Conjecture for Certain Abelian Varieties over Finite Fields

Details The Tate Conjecture for Certain Abelian Varieties over Finite Fields The Tate Conjecture for Certain Abelian Varieties over Finite Fields

1999-11-27

arxiv.org/abs/math/9911218v1

Mathematics

Number Theory

28 pages

Scientific paper

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.

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