Albanese kernels and Griffiths groups

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 $(C \times S)$ of a modification of the graph of the embedding $C ↪ S$ 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

Vol. 3, No. 3, 2021

Bruno Kahn

Appendix: Yves André

Abstract

PDF Access Denied

Keywords

Mathematical Subject Classification

Milestones

Authors