A remark on a $3$-fold constructed by Colliot-Th\'el\`ene and Voisin
Algebraic Geometry
2018-12-11 v3
Abstract
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 -fold which gives the negative answer in codimension if the generalized Bloch conjecture holds for a -fold constructed by Colliot-Th\'el\`ene and Voisin in the context of the study of the defect of the integral Hodge conjecture in degree .
Cite
@article{arxiv.1805.01067,
title = {A remark on a $3$-fold constructed by Colliot-Th\'el\`ene and Voisin},
author = {Fumiaki Suzuki},
journal= {arXiv preprint arXiv:1805.01067},
year = {2018}
}
Comments
11 pages, comments are welcome, v3. the exposition is improved; a section on stably birational invariants is added; an appendix on the Roitman theorem for the Walker maps and decomposition of the diagonal is added; to appear in Mathematical Research Letters