ABSTRACT
Let X be a complex space, Λ·X = E·˜X ⊕ Λ·E ⊕ Λ·˜E(−1) an element of R(X) as in chapter 2. In the present chapter we introduce three filtrations on Λ·X : the weight filtration W , the Hodge filtration F and its conjugate F¯ . They are defined by induction on the dimensions of the spaces; they are supposed to be already defined on Λ·E and Λ·˜E , on the other hand they are known for the De Rham complex E·˜
X . So we define the filtrations on Λ·X as direct sums
(up a shift on Λ·˜ E
in the case of the weight filtration). The above filtrations induce corresponding filtrations on the complex of global sections Γ
( X,Λ·X
) and on the cohomology Hk(X,C).
