The Hodge conjecture for powers of K3 surfaces of Picard number 16
arXiv:2203.09778
Abstract
We study the Hodge conjecture for powers of K3 surfaces and show that if the Kuga--Satake correspondence is algebraic for a family of K3 surfaces of generic Picard number 16, then the Hodge conjecture holds for all powers of any K3 surface in that family.
29 pages, to appear on the Michigan Mathematical Journal