English

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".

Keywords

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

R2 v1 2026-07-22T17:44:18.245Z