Abstract:
Hodge theory provides the notion of Hodge structure and of Hodge
class on a compact Kaehler manifold. In the general Kaehler context, we
proved that Hodge classes may not be related to complex geometry. We shall
explain in this talk why the Hodge conjecture has a completely different
flavour in algebraic geometry, and some evidences for it coming from the
study of Hodge loci.