On the Tate and Standard Conjectures over Finite Fields

2019/07/09 by Milne, James S
#14C25 11G09 #Algebraic Geometry (math.AG) #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1907.04143

Abstract

For an abelian variety over a finite field, Clozel (1999) showed that l-homological equivalence coincides with numerical equivalence for infinitely many l, and the author (1999) gave a criterion for the Tate conjecture to follow from Tate's theorem on divisors. We generalize both statements to motives, and apply them to other varieties including K3 surfaces.

Related

• The Tate and Standard Conjectures for Certain Abelian Varieties
• The Tate Conjecture for Motivic Endomorphisms of K3 Surfaces over Finite Fields
• Tate Conjecture And Finiteness of Abelian Varieties over Finite Field
• Homomorphisms of abelian varieties over geometric fields of finite characteristic
• The Tate conjecture over finite fields (AIM talk)