On the geometry of a smooth model of a fibre product of families of K3 surfaces

Abstract

The Hodge conjecture on algebraic cycles is proved for a smooth projective model of a fibre product of nonisotrivial 1-parameter families of K3 surfaces (possibly with degeneracies) over a smooth projective curve under the assumption that, for generic geometric fibres and , the ring is an imaginary quadratic field, , and is a totally real field or else .Bibliography: 10 titles.