The galois-cohomology tag has no wiki summary.
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Group Cohomology Vs Profinite group Cohomology
What is the difference of the group cohomology and the profinite group cohomology? I think one reason is that in the profinite group situation, the G-module must be continuous. Does any other ...
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Motivation for the relations defining $H^1(G,A)$ for non-commutative cohomology
First let me review the definition of first non-commutative cohomology. Let $G$ be a group and $A$ a left $G$-group, i.e. for any $\sigma, \tau\in G$ and $a, b\in A$, one has ...
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Galois groups of maximal unramified extensions
I have been workin throught Cassels-Frohlich Algebraic number theory. Im looking at local fields and their cohomology, in particular the Brauer group. On page 133 of casses-frohlich they make the ...
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Why do the two topologies on a Galois group coincide?
In the following one is referred to the book.
At this page, the author defines Krell topology on a Galois group(not necessarily finite); at the 22-th page of the same book, the quthor defines then the ...
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Question on $\operatorname{res}^G_U \circ \operatorname{cor}^U_G = N_{G/U}$
This is probably a very basic question, but I can't wrap my head around it.
Given a normal open subgroup $U$ of a profinite group $G$ and a $G$-Module $A$ we have the following equation in group ...
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Suggestions for a thesis in the area of Galois Cohomology [closed]
I'm just about to start my final year of undergrad. I need to choose a
thesis title but I'm having some trouble. I know a little Galois Cohomology
and would really like to learn more. The prof who is ...
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1answer
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Local invariants of the discrete Galois module associated to a $p$-ordinary newform
Let $f=\sum_{n=1}^\infty a_nq^n$ be a $p$-ordinary newform of weight $k\geq 2$, level $N$, and character $\chi$, and let $\rho_f:G_\mathbf{Q}\rightarrow\mathrm{GL}_2(K_f)$ be the associated $p$-adic ...
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On Grunwald-Wang theorem
Consider (roughtly speaking) the following statements (the Grunwald-Wang theorem)
Theorem 1 (see here for details Wiki): Let $K$ be a number field and $x \in K$. Then under some conditions : $x$ is ...
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1answer
67 views
Lifting additive characters
Let $K$ a finite extension of $\mathbb{Q}_p$ ($p$ prime different from 2) and let $G_K$ the absolute Galois group of $K$.
Let $\bar{u} : G_K \longrightarrow \mathbb{F}_p$ a continuous additive ...
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2answers
174 views
Are absolute Galois groups compact topological groups
Let $T$ be a finite set of primes and let $K$ be the maximal extension of $\mathbf{Q}$ unramified outside $T$.
We have three Galois groups:
$G_{\mathbf{Q}} = ...
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projective profinite groups
I'm reading the first chapter of Serre's Galois Cohomology.
On p. 58, He gives two examples of projective profinite groups:
(a) the profinite completion of free (discrete) groups;
(b) the cartesian ...
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Why has the category of all discrete $G$-modules not enough projectives when $G$ is profinite?
I found this article about Galois Cohomology, http://www.math.uga.edu/~turkelli/Introduction%20to%20Galois%20Cohomology.pdf
In it, it says that, when $G$ is a profinite group and $\mathbf{C}_G$ is ...
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Galois cohomology of Unitary groups
From Hilbert 90 (or, more precisely, a generalisation thereof), we know that the first (Galois) cohomology group of $GL_n$ is trivial, no matter the field of definition. However, for unitary groups, ...
