Spectral sequences and mixed Hodge structures

In this chapter we collect some algebraic preliminaries, especially on spectral sequences and pure and mixed Hodge structures.

Let E be a vector space. An increasing filtration is an increasing sequence of subspaces

· · · ⊂WmE ⊂Wm+1E ⊂ · · · with ⋂

WmE = (0)

We will consider only finite filtrations, that is WmE = (0) and = E only for a finite number of m.