Comparison of spectral sequences involving bifunctors
K-Theory and Homology
2009-06-08 v5
Abstract
Suppose given functors A x A' -F-> B -G-> C between abelian categories, an object X in A and an object X' in A' such that certain conditions hold. We show that, E_1-terms exempt, the Grothendieck spectral sequence of the composition of F(X,-) and G evaluated at X' is isomorphic to the Grothendieck spectral sequence of the composition of F(-,X') and G evaluated at X. So instead of "resolving X' twice", we may just as well "resolve X twice".
Cite
@article{arxiv.math/0610457,
title = {Comparison of spectral sequences involving bifunctors},
author = {Matthias Kuenzer},
journal= {arXiv preprint arXiv:math/0610457},
year = {2009}
}
Comments
Typos in Secs. 8.1, 8.2 corrected. Appeared in Documenta Math. 13, 677-737, 2008