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 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.

28 pages

Cited by in corpus (5)

• The Tate conjecture over finite fields (AIM talk)
• The full faithfulness conjectures in characteristic p
• On the multiplicities of a motive
• The fullness conjectures for products of elliptic curves
• Remark on nondegeneracy of simple abelian varieties with many endomorphisms