On the Hodge conjecture for products of certain surfaces

Mathematics – Algebraic Geometry

Scientific paper

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Scientific paper

In this paper we prove the Hodge conjecture for products of the form $S_1
\times ... S_n$, where $S_i$ are smooth projective surfaces such that
$p_g(S_i)=1, q(S_i)=2$. We also prove the Hodge conjecture for arbitrary
self-products of a K3 surface $X$ such that $End_{hodge}(T(X))$ is a CM number
field.

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