The aim of this work is to develop the program proposed by S. Bloch, L. Barbieri-Viale and V. Srinivas of generalizing Deligne mixed Hodge structures providing a new cohomology theory for complex algebraic varieties. In other words to construct and study cohomological invariants, of (proper) complex algebraic schemes, which are finer than the associated mixed Hodge structures in the case of singular spaces
