Mathematical Research Letters

Volume 27 (2020)

Number 1

A remark on a $3$-fold constructed by Colliot–Thélène and Voisin

Pages: 301 – 317



Fumiaki Suzuki (Department of Mathematics, University of Illinois, Chicago, Il., U.S.A.)


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–Thélène and Voisin in the context of the study of the defect of the integral Hodge conjecture in degree $4$.

Received 13 June 2018

Accepted 14 November 2018

Published 8 April 2020