All Questions
Tagged with spectral-sequences homological-algebra
114 questions
6
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0
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On the multiplicative structure in spectral sequences.
Let $f\colon X \rightarrow Y$ be a continuous map of sufficiently nice
topological spaces (say, smooth manifolds). Let ${\cal F}=(\dots\rightarrow
F_i \rightarrow F_{i+1}\to \dots)$ be a bounded ...
- 21.8k
4
votes
0
answers
1k
views
Grothendieck spectral sequence [duplicate]
Possible Duplicate:
Composing left and right derived functors
Hi,
probably this question is obvious. I apologize for this.
Given functors $F$ and $G$ left exact, with as good properties as you ...
- 51
128
votes
12
answers
12k
views
Spectral sequences: opening the black box slowly with an example
My friend and I are attempting to learn about spectral sequences at the moment, and we've noticed a common theme in books about spectral sequences: no one seems to like talking about differentials.
...
- 13.5k
3
votes
2
answers
493
views
Is the first filtration Hausdorff?
Maybe this is too technical and elementary, but I cannot make up my mind, nor find a reference.
The situation is the following: let $X$ be a double cochain (right half-plane) complex of abelian ...
- 1,975
2
votes
1
answer
247
views
Colimit of intersections
Let $B_i^p$ be a family of sets, where $p\in \mathbb{N}$ and $i \in I$, $I$ being a directed set, and such that, for every $i$, we have a descending chain of inclusions
$$
\dots \supset B_i^{p-1} \...
- 1,975
3
votes
1
answer
678
views
Convergence of right half-plane spectral sequence bounded on the right
This is a sequel to my previous question colimits of spectral sequences .
I think I've found the answer in S.A. Mitchell's paper "Hypercohomology spectra and Thomason's descent theorem". There the ...
- 1,975
5
votes
1
answer
918
views
colimits of spectral sequences
I'm looking for some references about colimits of spectral sequences.
More precisely: let $X : I \longrightarrow \cal{C}$ be a functor from a filtered category $I$ to the category of double cochain ...
- 1,975
4
votes
1
answer
2k
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Tensor product of spectral sequences?
I'm wondering about a cross product for spectral sequences. I've got an idea, and I wonder if it is written up anywhere, or if it even holds water.
Let's start with three spectral sequences, $E, F$ ...
- 12.5k
44
votes
19
answers
16k
views
introductory book on spectral sequences
I have studied some basic homological algebra. But I can't send to get started on spectral sequences. I find Weibel and McCleary hard to understand.
Are there books or web resources that serve as ...
5
votes
1
answer
3k
views
Question about hypercohomology / spectral sequence of a complex of "almost-acyclic" sheaves
I have a very particular situation involving a (non-exact) complex $K$ of coherent sheaves on a nonsingular projective variety $X$, and I need to compute the hypercohomology of the complex. The ...
- 545
8
votes
1
answer
1k
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Convergence of spectral sequences of cohomological type
Following the first chapter of Hatcher's great book "Spectral Sequences in Algebraic Topology", I got into problems with spectral sequences of cohomological type. Fix a ring $R$ once and for all. ...
- 727
6
votes
1
answer
890
views
Serre spectral sequence with spectra
A friend recently asked me if i had heard anything about a stable Serre Spectral Sequence or one constructed with spectra, has any one else ever heard of this? is there any reason other than ...
- 3,726
8
votes
1
answer
2k
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How does one get the short exact sequence in a two-column spectral sequence?
In a two-column double complex, one gets from the associated spectral sequence short exact sequences $0\to E_2^{1,n-1}\to H^n\to E_2^{0,n}\to 0$, where $H^n$ is the cohomology of the total complex, ...
- 1,488
56
votes
5
answers
9k
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Why are spectral sequences so ubiquitous?
I sort of understand the definition of a spectral sequence and am aware that it is an indispensable tool in modern algebraic geometry and topology. But why is this the case, and what can one do with ...
- 25.6k