The Hodge conjecture for a certain class of singular varieties

Abstract

In [J] there is stated a version of the Hodge conjecture for complex singular varieties (reduced separated algebraic schemes over C), generalizing the popular version of the conjecture. A statement of the general Hodge conjecture for the singular case, extending the amended version by Grothendieck, is given in [L2], using the techniques in [J]. The statement is this. Let Z be a reduced separated algebraic scheme over C. The lowest weight part W−i Hi (Z ,Q) of the BorelMoore homology Hi (Z ,Q) defines a Hodge structure of weight −i . Recall the filtration by niveau, given by