2
votes
0answers
37 views

$\operatorname{Br}(\Bbb Q_{47})$

I'm looking for division algebras over $\Bbb Q_{47}$. I guess my best bet is to calculate the Brauer group $\operatorname{Br}(\Bbb Q_{47})$. What's the best way of performing this calculation? Should ...
1
vote
0answers
55 views

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 ...
6
votes
2answers
142 views

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 ...
2
votes
0answers
112 views

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 ...
2
votes
0answers
129 views

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 ...
2
votes
2answers
260 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}} = ...
20
votes
0answers
212 views

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: the profinite completion of free (discrete) groups; the cartesian product ...