Questions tagged [spectral-sequences]

Question 1

As in this question, I have trouble with this part of Bott and Tu's Differential Forms in Algebraic Topology : The Spectral Sequence of a Double Complex. The starting point is a double complex $K=\...

Question 2

Let $X$ be a topological/smooth/complex etc. manifold and $G \subset \text{Aut}(X)_{\text{top, smooth, complex}}$ a finite group acting faithfully on $X$ as homeomorphsms/diffeomorphisms/holomorphic ...

Question 3

Let $F\to E \to B$ be a fiber bundle and assume it satisfies all conditions that Serre spectral sequence asked. Then we have $E_2^{p,q}=H^p(B,H^q(F))$ $E_2^{p,q}\Rightarrow H^n(E)$ Since the second ...

Question 4

I am studying the book "Spectral Sequences" by John Rognes. I arrived at the chapter about cohomological spectral sequences and had some confusion (which I think appeared also in the ...

Question 5

I currently started studying spectral Sequences with the book of John Rognes. In his first chapter he defines Spectral Sequences as a sequence of bigraded abelian groups with differentials of certain ...

Question 6

Let $R$ be a commutative ring and $\{E^{r \ge 2}_{p,q}, d^r\}_{r,p,q}$ a spectral sequence of $R$-modules (...where the next page is obtained from the previous via the rule $E^{r+1}_{p,q} = \...

Question 7

I am reading this paper: https://msp.org/pjm/2017/290-2/p08.xhtml. In Section 4, the authors compute several examples of the LHS spectral sequence with $\mathbb{C}^*$ coefficients. The method they use ...

Question 8

The Brown-Gersten spectral sequence, from the proceedings Algebraic K-theory I (1972), states $E_2^{pq}=H^p(X, \pi_{-q}K) \Rightarrow \pi_{-p-q}R\Gamma(X,K)$ for a simplicial presheaf $K$ which ...

Question 9

I feel like I'm completely begginer about Spectral sequence. Definition F.102. ( Gortz, Wedhorn's Algebraic Geometry, Vol.2 ) Let $(E_r , d_r)_{r\ge r_0}$ be a bounded spectral sequence in $\mathcal{...

Question 10

In Parker: Higher extensions between modules for $SL_2$ (link), the author constructs some version of LHS spectral sequence. He has an interesting corollary. Corollary 2.3: Suppose the $d_0$ are all ...

Question 11

Let $R$ be a connective commutative ring spectrum, and let $A$ and $B$ be connective $R$-modules. Then there is a first-quadrant homological spectral sequence $$E^2_{p,q}=\bigoplus_{s+t=q}\mathrm{Tor}...

Question 12

Let $R$ be a commutative ring. $E_0^{p,q}$ be a first-quadrant spectral sequence induced by a double complex of $R$-modules (cohomology) and $E_r^{p,q} \implies H^{p+q}$. Assume at the second page $...

Question 13

As the title says, I am looking for the reference that the Grothendieck spectral sequence is functorial in the input. I looked at Weibel and other classical sources but they do not provide this. I ...

Question 14

Disclaimer: I'm not an expert in étale cohomology. This just came up, when trying to generalize a method, that came up studying a problem in algebraic number theoy/ class field theoy. Let $f:Y\to X$ ...

Question 15

If $k$ is a field, $G$ is a group, and $Z \leq G$ is a central subgroup, the Lyndon-Hochschild-Serre spectral sequence for cohomology with coefficients in the trivial module $k$ has $E_2$-page which ...

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Questions tagged [spectral-sequences]

How are defined these double complexes in Bott Tu, Section 14?

Comparison Invariant Cohomology with Cohomology of Quotient Manifold

How can we understand a homomorphism induced by Serre spectral sequence?

Understanding convergence of spectral sequences

Motivation for Spectral Sequences

Finitely Generatedness Issues in Spectral Sequences

Obtaining the LHS spectral sequence with $\mathbb{C}^*$ coefficients from the LHS spectral sequence with $\mathbb{Z}_2$ coefficients

Homotopical framework of two spectral sequences

Question about hypercohomology spectral sequence in algebraic geometry ( Gortz, Wedhorn's Vol.2. )

Does the spectral sequence stabilize on second page if vertical differentials in a double complex are zero?

What is the algebra structure on homotopy groups used in the Künneth spectral sequence? [closed]

Spectral sequences with vanishing diagonals behaving asymmetrically.

Reference for functoriality of Grothendieck spectral sequence

Exactness of a sequence arising from the Hochschild-Serre sequence in étale cohomology

Reference request: E_2-page for Lyndon-Hochschild-Serre SS for central extension

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