Some spectral sequences for filtered complexes and applications
Let \(f: {\mathcal A}\to {\mathcal A}'\) be a left exact functor between abelian categories, such that \(\mathcal A\) has enough injectives, and let \(C\in \mathcal A\) be a filtered complex. A series of spectral sequences converging to the derived functors of \(f\) applied to \(C\) are obtained as the derived functors of \(f\) applied to the complexes given by Deligne's shift procedure. As an application, the author obtains a Leray spectral sequence for the de Rham cohomology and a comparison with the Leray spectral sequence for singular cohomology, as well as a comparison between Bloch-Ogus coniveau spectral sequences and Leray spectral sequences induced by the canonical map from a site which is finer than the Zariski site.
scientific article; zbMATH DE number 1013953