ABSTRACT. We construct a heirarchy of spectral sequences for a filtered complex 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 isomorphism 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.

Date: 20 Aug 1994.

1991 Mathematics Subject Classification. 14J.

Key words and phrases. de Rham cohomology, Leray spectral sequence, Bloch-Ogus spectral sequence.