Varieties with representable CH₀-group and a question of Colliot-Thélène

2025/08/04 by Voisin, Claire
#Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2508.02331

Abstract

We continue our investigation of the geometry of the Albanese morphism on 0-cycles. We provide an example of a smooth projective variety with representable CH₀-group but with no universal 0-cycle, which answers a question asked by Colliot-Thélène. Our construction relies on a counterexample to the integral Hodge conjecture provided by Benoist and Ottem.

Citations

• Matroids and the integral Hodge conjecture for abelian varieties
• Cycle classes on abelian varieties and the geometry of the Abel-Jacobi map
• Geometric representability of 1-cycles on rationally connected threefolds
• Integral Fourier transforms and the integral Hodge conjecture for one-cycles on abelian varieties
• A pencil of Enriques surfaces with non-algebraic integral Hodge classes
• Special subvarieties arising from families of cyclic covers of the projective line
• Elliptic Surfaces
• Families of rationally connected varieties

Related

• Notes sur l'application d'Albanese pour les zéro-cycles
• The universal regular quotient of the Chow group of 0-cycles on a\n singular projective variety
• Divisibility Results for zero-cycles
• Zero-cycles on quasi-projective surfaces over p-adic fields
• Étale degree map and 0-cycles