Complex varieties with infinite Chow groups modulo 2

2015/02/06 by Totaro, Burt
#14C15 #14J30 #14K05 #Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1502.02071

Abstract

We show that for a very general principally polarized complex abelian 3-fold, the Chow group of algebraic cycles is infinite modulo every prime number. In particular, this gives the first examples of complex varieties with infinite Chow groups modulo 2.

Related

• Non-divisible cycles on products of very general Abelian varieties
• The Chow group mod ℓ for a product of elliptic curves
• Varieties over ℚ with infinite Chow groups modulo almost all primes
• The cycle class of the supersingular locus of principally polarized abelian varieties
• Higher Chow groups and not necessarily admissible cycles