2025/04/30 by Jean-Louis Colliot-Thélène, Colliot-Thélène, Jean-Louis
Mathematics · #14C25 #14C35 #14E08 #14M22 #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Commutative Algebra and Its Applications #FOS: Mathematics
paper · pdf · doi:10.48550/arxiv.2504.21726
openalex publication_date 2025/04/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
For a smooth projective variety X over an arbitrary field k, we discuss the surjectivity of the Albanese map from the Chow group of zero-cycles of degree zero on X to the group of rational points of the Albanese variety of X. Over arithmetic fields, we use Severi-Brauer fibrations to produce examples where the map is not surjective. For varieties X over the complex field, we discuss the question after extension of the complex field to function fields of varieties. This is related to C. Voisin's notion of universal zero-cycle and to rationality questions for rationally connected threefolds.