Timeline for On the multiplicative structure in spectral sequences.
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| Aug 12, 2011 at 9:39 | comment | added | asv | @some guy on the street: Perhaps it depends on what you mean by "fundamentally different". To me it looks rather different. But perhaps for experts in homological algebra/alg. geometry the two situations are very similar modulo "common knowledge". | |
| Aug 11, 2011 at 17:44 | comment | added | some guy on the street | Is this fundamentally a different question from the convergence of a spectral sequence of algebras to a desired algebra? In re. your last remark, the hypercohomology s.s. is asserted on p.515 of "A User's Guide to S.S." By McCleary; two methods of proof are suggested --- composite functor s.s. OR a double complex of injective objects whose total complex has some desired homology. | |
| Aug 11, 2011 at 8:45 | comment | added | asv | @Mark Grant: Bredon in section IV.6.5 deals with the Leray spectral sequence. This is not what I mentioned. I need one of the so called hypercohomology spectral sequences, see wikipedia en.wikipedia.org/wiki/Hyperhomology_spectral_sequence | |
| Aug 11, 2011 at 7:30 | comment | added | asv | @Donu Arapura: Thanks. I have checked pp. 113-115 in Voisin's book. Apparently she deals with a different spectral sequence. To compute the push-forward of a complex of sheaves there are two different spectral sequences. They come from two different filtrations on a bi-complex of injective sheaves resolving the given complex. (Also in my case I have described E_1 rather than E_2.) | |
| Aug 10, 2011 at 14:19 | comment | added | Mark Grant | Also have you checked out Bredon's "Sheaf theory", section IV.6.5? | |
| Aug 10, 2011 at 11:24 | comment | added | Donu Arapura | It is certain true in general! As for references, the only thing I can suggest at the moment is Voisin's "Hodge theory and complex...II" pp 113-115. This is worked for $\mathbb{Z}$ coefficients, but it's better than nothing. (By the way, it is an $E_2$ spectral sequence.) | |
| Aug 10, 2011 at 9:25 | comment | added | asv | @Mark Grant: In fact I need to use this fact in a paper, potential readers of which will not be experts in homological algebra or algebraic geometry, but analysts and possibly differential geometers. In these communities the above fact is not a common knowledge. So some background reference would be helpful. | |
| Aug 10, 2011 at 9:17 | history | edited | asv | CC BY-SA 3.0 |
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| Aug 10, 2011 at 9:08 | comment | added | Mark Grant | I would guess that once you work out all the details yourself, the need for a reference will magically disappear (cf the experts you asked)! (Sorry for the annoying comment :) | |
| Aug 10, 2011 at 8:38 | comment | added | asv | @Mark Grant: yes, I did. I could not find it there too. | |
| Aug 10, 2011 at 8:08 | comment | added | Mark Grant | Have you tried the book of Godement, "Topologie algébrique et théorie des faisceaux"? | |
| Aug 10, 2011 at 8:06 | history | edited | asv | CC BY-SA 3.0 |
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| Aug 10, 2011 at 8:01 | history | edited | asv | CC BY-SA 3.0 |
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| Aug 10, 2011 at 7:55 | history | asked | asv | CC BY-SA 3.0 |