Deformation of algebraic cycle classes in characteristic zero

Spencer Bloch, Hélène Esnault, Moritz Kerz

Published 2013-10-07, updated 2014-02-24Version 2

We study a formal deformation problem for rational algebraic cycle classes motivated by Grothendieck's variational Hodge conjecture. We argue that there is a close connection between the existence of a Chow-K\"unneth decomposition and the existence of expected deformations of cycles. This observation applies in particular to abelian schemes.