Timeline for isomorphic spectral sequences => quasi-isomorphic filtered chain complexes?

9 events

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Apr 21, 2017 at 4:54	history	edited	მამუკა ჯიბლაძე	CC BY-SA 3.0	tex
Jun 20, 2012 at 23:14	vote	accept	Vidit Nanda
Jun 20, 2012 at 19:10	answer	added	Tyler Lawson		timeline score: 14
Jun 20, 2012 at 18:29	comment	added	Donu Arapura		Well, a morphism of filtered complexes which induces an isomorphism at the $E_1$ level (which implies it all the way down) is the same thing as a filtered quasi-isomorphism = isomorphism in the filtered derived category. Although this may not answer your question.
Jun 20, 2012 at 18:09	comment	added	Vidit Nanda		Donu, I agree that it seems strong. But the question is natural: in the filtered derived category, does the equivalence $C \sim C'$ iff $E(C)$ is isomorphic to $E(C')$ go by another name?
Jun 20, 2012 at 17:58	comment	added	Donu Arapura		I realized you're only asking for isomomorphisms, nevertheless, it feels too strong.
Jun 20, 2012 at 17:56	comment	added	Donu Arapura		In other words, is the map from the filtered derived category to the category of spectral sequences full? I doubt it, although I don't have a counterexample.
Jun 20, 2012 at 17:52	answer	added	Ralph		timeline score: 7
Jun 20, 2012 at 17:34	history	asked	Vidit Nanda	CC BY-SA 3.0