All Questions
Tagged with spectral-sequences homological-algebra
114 questions
6
votes
1
answer
858
views
What kind of spectral sequences come from double complexes?
Given a double complex in the first quadrant, one can derive from it a (homological or cohomological) spectral sequence converging to the (co)homology of the total complex of the double complex.
My ...
- 20.9k
6
votes
1
answer
1k
views
Unbounded complexes, resolutions and computation of derived functors
Hey guys, let $F: \mathcal{A} \rightarrow \mathcal{B}$ be a left exact functor between abelian categories with enough injectives, let $K \in Kom(\mathcal{A})$ be an unbounded complex, I've heard that ...
CommunityBot
- 1
4
votes
2
answers
1k
views
Tracking spectral sequence differentials
I read a number of posts here on MO, but haven't quite found an answer to the question of where the differentials in a spectral sequence come from.
I came across a differential $d^{0,1}$ on the $E_2$-...
CommunityBot
- 1
5
votes
1
answer
1k
views
Inverse limit of spectral sequences
I find myself in the following situation:
I have a sequence of first quadrant spectral sequences, let's call them $ E(n)_{p,q}^* $, each convergent to $E(n)_{p,q}^\infty$, with spectral sequence ...
- 15.6k
6
votes
0
answers
723
views
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 ...
CommunityBot
- 1
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 ...
- 13.5k
56
votes
5
answers
9k
views
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 ...
- 56.6k
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 ...
CommunityBot
- 1
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} \...
CommunityBot
- 1
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 ...
CommunityBot
- 1
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 ...
- 27k
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 ...
- 27.7k
8
votes
1
answer
2k
views
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, ...
- 47.3k