Mixed Hodge complexes on algebraic varieties and t-structures

The aim of this paper is to provide some complements on the categories of mixed QQ-Hodge complexes introduced by M. Saito in [17]. In particular we prove that the category of pure diagrams has a t-structure that lifts the perverse t-structure and derive some consequences of this fact. We also compare the category of mixed Hodge complexes defined by M. Saito with a more naive version. These complements are used in [12] to provide a partial generalization to higher dimension of a result of A. Beĭlinson [1] and [2] which shows that the derived category of polarizable mixed Hodge structures is equivalent to the more flexible triangulated category of polarizable mixed Hodge complexes.