On algebraic cohomology classes on a smooth model of a fiber product of families of \(K3\) surfaces (Q2343919)

The author proves the Hodge conjecture for smooth projective models of the fiber product of non-isotrivial one-parameter families of \(K3\) surfaces \(X_1\) and \(X_2\) under certain assumptions on the ranks of the transcendental lattices and on the representations of the Hodge groups of the general geometric fibers of the families \(X_1\) and \(X_2\).