Search Results
| Search type | Search syntax |
|---|---|
| Tags | [tag] |
| Exact | "words here" |
| Author |
user:1234 user:me (yours) |
| Score |
score:3 (3+) score:0 (none) |
| Answers |
answers:3 (3+) answers:0 (none) isaccepted:yes hasaccepted:no inquestion:1234 |
| Views | views:250 |
| Code | code:"if (foo != bar)" |
| Sections |
title:apples body:"apples oranges" |
| URL | url:"*.example.com" |
| Saves | in:saves |
| Status |
closed:yes duplicate:no migrated:no wiki:no |
| Types |
is:question is:answer |
| Exclude |
-[tag] -apples |
| For more details on advanced search visit our help page | |
Results tagged with group-cohomology
Search options not deleted
user 4149
In mathematics, group cohomology is a set of mathematical tools used to study groups using cohomology theory, a technique from algebraic topology. Analogous to group representations, group cohomology looks at the group actions of a group G in an associated G-module M to elucidate the properties of the group.
2
votes
Compute corestriction map on group cohomology in Magma
Since OP found my comments helpful, I post them as an answer to have an editable text.
Let $G$ be a group, $H\subset G$ be a subgroup of finite index,
and $M$ be a right $H$-module.
I know an explicit …
- 14.2k
6
votes
Hilbert's Satz 90 for real simply-connected groups?
In addition to the answer of Gro-Tsen: Let $G=\operatorname{SU}(3)$. Then $H^1({\mathbb R},G)$ classifies matrices of Hermitian forms in 3 variables with determinant 1. There are two equivalence class …
- 14.2k
1
vote
1
answer
232
views
Transfer for the group of coinvariants: a reference request
Let $G$ be a group and $M$ be a $G$-module,
that is, an abelian group written additively on which $G$ acts:
$$ (g,m)\mapsto g m.$$
We consider the group of coinvariants
$$ M_G:=G/\langle g m -m\ |\ g\ …
- 14.2k
6
votes
2
answers
264
views
Group homology for a metacyclic group
Let $G$ be a finite group, and let $M$ be a finitely generated $G$-module,
that is, a finitely generated abelian group on which $G$ acts.
We work with the first homology group
$$ H_1(G,M).$$
For any c …
- 14.2k
9
votes
1
answer
369
views
For which subgroups the transfer map kills a given element of a group?
$\newcommand{\ab}{{\rm ab}}
\newcommand{\ord}{{\rm ord}}
$Let $G$ be a finite or profinite group. Consider the abelianized group
$$G^\ab=G/G'$$
where $G'$ is the commutator subgroup of $G$.
Let $H\sub …
- 14.2k
6
votes
Accepted
The second Tate-Shafarevich group of a permutation module is trivial
We write $G_w={\rm Gal}(L_w/K_v)$.
Definition. For $n\ge 1$, we denote
$$Ш_\omega^n(G,M)=\ker\Big(H^n(G,M)\to\prod_C H^n(C,M)\Big)$$
where $C$ runs over the cyclic subgroups of $G$.
Remark. $Ш^2(L …
- 14.2k
4
votes
0
answers
160
views
Algorithm for generalized Hilbert's Theorem 90 over $\Bbb R$
$\newcommand{\GL}{\operatorname{GL}}
\newcommand{\R}{{\Bbb R}}
\newcommand{\C}{{\Bbb C}}
$For a natural number $n$, let $z\in \GL(n,\C)$ be a 1-cocycle
of $G=\GL_{n,\R}\,$, that is,
an invertible comp …
- 14.2k
6
votes
1
answer
176
views
Restriction vs. multiplication by $n$ in Tate cohomology
$\DeclareMathOperator{\Res}{Res}
\DeclareMathOperator{\Cor}{Cor}$
This question was asked in MSE.
It got no answers or comments, and so I post it here.
Let $H$ be a subgroup of a finite group $G$, and …
- 14.2k
3
votes
1
answer
291
views
The torsion subgroup of the coinvariants for a $G$-module
Let $G$ be a finite group and $M$ be a finitely generated $G$-module,
that is, a finitely generated abelian group on which $G$ acts.
Consider the functor
$$ (G,M)\rightsquigarrow F(G,M):= (M_G)_{\rm T …
- 14.2k
6
votes
0
answers
483
views
The Tate-Nakayama theorem and inflation
Let $K$ be a nonarchimedean local field,
and $L/K$ be a finite Galois extension with Galois group $G={\rm Gal}(L/K)$ of order $n=[L:K]$.
By local class field theory, there is a canonical isomorphism
$ …
- 14.2k
1
vote
0
answers
163
views
Inflation in degrees $0$, $-1$, and $-2$ for Tate cohomology of finite groups
Let $\pi\colon G'\to G$ be a surjective homomorphism of finite groups, and let $A$ be a $G$-module.
I need explicit formulas for the inflation maps
$${\rm Inf}^{r}\colon H^{r}(G,A)\to H^{r}(G',A)$$ fo …
- 14.2k
2
votes
0
answers
166
views
Cup product in modified (Tate) group hypercohomology
Let $G$ be a finite group.
Let
$$ M^\bullet=\,(\dots\to M^{-1}\to M^0\to M^1\to\dots) $$
be a bounded complex of $G$-modules.
One can define Tate hypercohomology groups $H^n(G,M^\bullet)$ for all $n\i …
- 14.2k
0
votes
Quasi-isomorphism preserves group hypercohomology
I give an elementary proof of the fact that a quasi-isomorphism of short complexes (complexes of length 2) of $\Gamma$-modules induces an isomorphism on hypercohomology.
Actually, it is very close to …
- 14.2k
3
votes
2
answers
333
views
Quasi-isomorphism preserves group hypercohomology
I am looking for a reference for the assertion in the title.
In more detail, let $\Gamma=\{1,\gamma\}$ be a group of order 2.
Let $A$ be a $\Gamma$-module (an abelian group on which $\Gamma$ acts).
T …
- 14.2k
4
votes
0
answers
117
views
Neutral cohomology classes and restriction maps for $H^2$ in group cohomology
$\DeclareMathOperator\res{res}$
Let $G$ be a profinite group.
Let $A$ be a finite $G$-group (a finite group on which $G$ acts continuously), not necessarily abelian,
with center $Z=Z(A)$.
We say that …
- 14.2k