A remark on a 3-fold constructed by Colliot-Thelene and Voisin

摘要

A classical question asks whether the Abel-Jacobi map is universal among all regular homomorphisms. In this paper, we prove that we can construct a 4-fold which gives the negative answer in codimension 3 if the generalized Bloch conjecture holds for a 3-fold constructed by Colliot-Thelene and Voisin in the context of the study of the defect of the integral Hodge conjecture in degree 4.