Some spectral sequences for filtered complexes and applications

Abstract

We construct a hierarchy 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 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.