Polarizations and Grothendieck's Standard Conjectures

2001/03/31 by J. S. Milne · 1 citation
Mathematics · #math.AG #math.NT #msc:14K99 #msc:11G99

paper · pdf

published as Ann. of Math. (2), Vol. 155 (2002), no. 2, 599--610 · 12 pages published version

arxiv created 2004/06/02 · arxiv updated 2009/11/30

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.

Cited by

• Standard conjecture of Hodge type for powers of abelian varieties

Related

• Hodge classes on abelian varieties
• The Tate and Standard Conjectures for Certain Abelian Varieties
• Polarizations on abelian varieties
• A Survey of the Hodge Conjecture for Abelian Varieties
• A survey around the Hodge, Tate and Mumford-Tate conjectures for abelian varieties