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.

DOI
http://doi.org/10.2307/3062126

Authors

John S. Milne