Vol. 3, No. 3, 2021

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Albanese kernels and Griffiths groups

Bruno Kahn

Appendix: Yves André

Vol. 3 (2021), No. 3, 589–656
Abstract

We describe the Griffiths group of the product of a curve C and a surface S as a quotient of the Albanese kernel of S over the function field of C. When C is a hyperplane section of S varying in a Lefschetz pencil, we prove the nonvanishing in Griff(C × S) of a modification of the graph of the embedding CS for infinitely many members of the pencil, provided the ground field k is of characteristic 0, the geometric genus of S is > 0, and k is large or S is “of motivated abelian type”.

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Keywords
Albanese kernel, Griffiths group, motive
Mathematical Subject Classification
Primary: 14C25, 14D06
Milestones
Received: 22 April 2020
Revised: 12 August 2020
Accepted: 26 August 2020
Published: 13 May 2021
Authors
Bruno Kahn
IMJ-PRG
4 place Jussieu
Case 247
75252 Paris Cedex 5
France
Yves André
IMJ-PRG
4 place Jussieu
Case 247
75252 Paris Cedex 5
France