Polarizations and Grothendieck's Standard Conjectures

Abstract

We prove that Grothendieck's Hodge standard conjecture holds for abelian varieties in arbitrary characteristic if the Hodge conjecture holds for complex abelian varieties of CM-type. For abelian varieties with no exotic algebraic classes, we prove the Hodge standard conjecture unconditionally.

arXiv comment12 pages published version

References in corpus (1)

• Equivalence numérique et équivalence cohomologique pour les variétés abéliennes sur les corps finis