The Tate Conjecture for Certain Abelian Varieties over Finite Fields
Abstract
Tate's theorem (Invent. Math. 1966)implies that the Tate conjecture holds for any abelian variety over a finite field whose Ql-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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