Some spectral sequences for filtered complexes and applications

Abstract. We construct a heirarchy of spectral sequences for a filtered com-plex under a left-exact functor. As applications we prove (1) the existence of a Leray spectral sequence for de Rham cohomology, (2) the equivalence of this sequence with the “usual ” Leray spectral sequence under the comparison iso-morphism and (3) the isomorphism of the Bloch-Ogus spectral sequence with the Leray spectral sequence for the morphism from the fine site to the Zariski site. 1