0
votes
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43 views

First cohomology of a Galois group with finite base field

Let $l/k$ be a (may be infinite) galois extension with galois group $G$ and $k$ a finite field with size $q$. Also $k$ and $l$ are given the discrete topology. $G$ is given the Krull topology. Then ...
3
votes
0answers
48 views

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 the Krull topology on a Galois group (not necessarily finite); on the 22nd page of the same book, the author defines the ...
2
votes
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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 ...