Algebraic cycles on an abelian variety

2009/08/05 by O'Sullivan, Peter · 1 citation
#14C25 #14K05 (Primary) 18D10 (Secondary) #Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.0908.0626

Abstract

It is shown that to every Q-linear cycle αmodulo numerical equivalence on an abelian variety A there is canonically associated a Q-linear cycle αmodulo rational equivalence on A lying above α. The assignment α-> αrespects the algebraic operations and pullback and push forward along homomorphisms of abelian varieties.

Cited by

• Intersection complex of any threefold as a Chow motive

Related

• Torsion codimension 2 cycles on supersingular abelian varieties
• An equivalent condition for abelian varieties over finite fields to have QM
• A finiteness theorem for algebraic cycles
• Some new examples of smash-nilpotent algebraic cycles
• The arithmetic of QM-abelian surfaces through their Galois representations