Hodge classes on abelian varieties

2020/10/17 by Milne, James S.
#14K99 #Algebraic Geometry (math.AG) #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2010.08857

Abstract

We prove, following Deligne and André, that the Hodge classes on abelian varieties of CM-type can be expressed in terms of divisor classes and split Weil classes, and we describe some consequences. In particular, we show that Grothendieck's standard conjecture of Lefschetz type implies the Hodge conjecture for abelian varieties (Abdulali, André, ...).

Related

• Hodge classes on abelian varieties of low dimension
• A Survey of the Hodge Conjecture for Abelian Varieties
• Notes on absolute Hodge classes
• Polarizations and Grothendieck's Standard Conjectures
• The Tate and Standard Conjectures for Certain Abelian Varieties