Geodesic
On Algebraic Cohomology Classes on a Smooth Model of a Fiber Product of Families of K3 surfaces
Matematičeskie zametki, Tome 96 (2014) no. 5, pp. 738-746.

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Hodge's conjecture on algebraic cycles is proved for a smooth projective model $X$ of the fiber product $X_1\times_CX_2$ of nonisotrivial one-parameter families of K3 surfaces (possibly with degeneracies) under certain constraints on the ranks of the transcendental cycle lattices of the general geometric fibers $X_{ks}$ and representations of the Hodge groups $\operatorname{Hg}(X_{ks})$.
Keywords: Hodge's conjecture on algebraic cycles, K3 surface, smooth projective model. 
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O. V. Nikol'skaya. On Algebraic Cohomology Classes on a Smooth Model of a Fiber Product of Families of K3 surfaces. Matematičeskie zametki, Tome 96 (2014) no. 5, pp. 738-746. http://geodesic.mathdoc.fr/item/MZM_2014_96_5_a9/

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