# On the Hodge conjecture for products of certain surfaces

Research paper by José J. Ramón-Marí

Indexed on: 17 May '05Published on: 17 May '05Published in: Mathematics - Algebraic Geometry

#### Abstract

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.