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2 votes
0 answers
222 views

Grothendieck spectral sequence and exact couples

I'm thinking about the Grothendieck spectral sequence. I'm trying to understand how it relates to exact couples. Can anyone help me prove in general that the Grothendieck Spectral sequence converges ...
user avatar
1 vote
0 answers
160 views

Diagrams filled by the edge homomorphism of the Grothendieck spectral sequence

Suppose $A,B,C,D,Z$ are abelian categories. Let $G:C\longrightarrow D$, $F:D\longrightarrow Z$, $P:C\longrightarrow A$, $G':A\longrightarrow B$, $P':D\longrightarrow B$ and $F':B\longrightarrow Z$ are ...
Pritthijit Biswas's user avatar
3 votes
0 answers
277 views

Dimension three spectral sequences

If you have two triangulated functors $F,G$, you can compute the cohomology of $FG(-)$ in terms of the cohomology of $G(-)$ and the cohomology of $F(-)$, in terms of a ``Grothendieck spectral sequence'...
Pulcinella's user avatar
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5 votes
1 answer
425 views

Can we construct a filtered chain complex from a spectral sequence?

Suppose $\{(E_r,d_r)\}$ for $r>0$ forms a spectral sequence over a field $\mathbb{F}$, i.e. for any $r$, $(E_r,d_r)$ is a chain complex over $\mathbb{F}$ and $E_{r+1}=H(E_r,d_r)$. For simplicity, ...
Faniel's user avatar
  • 673
5 votes
1 answer
609 views

Functoriality of filtered spectral sequences

What is the appropriate functoriality statement of a filtered chain map between filtered spectral sequences? Suppose that we have two filtered chain complexes $C,C'$ and a filtered chain map $f\colon ...
Onkar Singh Gujral's user avatar
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 ...
unkn21's user avatar
  • 51
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} \...
Agustí Roig's user avatar
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