English

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 44-fold which gives the negative answer in codimension 33 if the generalized Bloch conjecture holds for a 33-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 44.

Keywords

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