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Mathematics > Algebraic Geometry

arXiv:1805.01067 (math)
[Submitted on 3 May 2018 (v1), last revised 8 Dec 2018 (this version, v3)]

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

Authors:Fumiaki Suzuki
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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 $4$-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 $4$.
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
Subjects: Algebraic Geometry (math.AG)
MSC classes: 14C25, 14C30, 14C35
Cite as: arXiv:1805.01067 [math.AG]
  (or arXiv:1805.01067v3 [math.AG] for this version)
  https://doi.org/10.48550/arXiv.1805.01067

Submission history

From: Fumiaki Suzuki [view email]
[v1] Thu, 3 May 2018 00:42:50 UTC (7 KB)
[v2] Wed, 13 Jun 2018 15:10:15 UTC (8 KB)
[v3] Sat, 8 Dec 2018 21:33:47 UTC (11 KB)
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