All Questions
Tagged with profinite-groups homological-algebra
8 questions
1
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0
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120
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Multiplicativity of Euler–Poincaré characteristics of cohomology of pro-$p$ groups
While reading a paper, I found a mentioning that for an extension $1 \rightarrow H \rightarrow G \rightarrow N \rightarrow 1$ of pro-$p$ groups, the Euler–Poincaré characteristics $\chi(H)$, $\chi(G)$,...
- 1,013
3
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0
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308
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Non-abelian group cohomology, additional information
Let $G$ be a (profinite) group, and let $M$ be a non-abelian $G$-module.
We know how to construct reasonably $H^0(G,M)$ and $H^1(G,M)$ and it turns out that $H^1(G,M)$ is just a pointed set and not ...
- 463
2
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0
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155
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Profinite projective and free modules
I am studying cohomology of profinite groups and the following question came to my mind: suppose we have $G$ a pro-$p$ group which is Poincaré Dual of dimension $d$. This means that $\mathbb{Z}_p$ as ...
- 767
4
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219
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Rational cohomology cohomology of $p$-adic analytic groups
It is a result of Lazard that given $G$ a compact $p$-adic analytic group then we have an isomorphism
\begin{equation} H^*(G; \mathbb{Q}_p) \cong H^*(T_eG; \mathbb{Q}_p) \end{equation}
where $T_eG$ is ...
- 767
2
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0
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285
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kernel and cokernel of corestriction map in cohomology of a profinite group
Let $G$ be a profinite group, $N$ a normal open subgroup and $A$ a discrete $G$-module. We have a corestriction map $cor: H^1(N, A)_{G/N} \to H^1(G, A)$. Are there any results on the kernel and ...
- 429
16
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0
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952
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Continuous cohomology of a profinite group is not a delta functor
Let $G$ be a profinite group, then there is a general notion of continuous cohomology groups $H^n_{\text{cont}}(G, M)$ for any topological $G$-module $M$ (I require topological $G$-modules to be ...
- 2,923
3
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259
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A question about continuous group cohomology
Let $G$ be a profinite topological group, $M$ a discrete $G$-module.
If $M$ is "P", is every $H^i_{\rm cont}(G,M)$ also "P"? or at least is it a subgroup/subquotient of an abelian group that is "P"? ...
user95222
7
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0
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320
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On an inequality concerning the strict cohomological dimension of a profinite group
This is an exercise from Serre’s book on Galois cohomology.
Let $G$ be a profinite group and $H$ a normal closed subgroup and suppose that the cohomological dimension at the prime $p$ of $G/H$ is ...
user44591