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Results tagged with group-cohomology
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user 17907
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.
1
vote
How to show an invariant subfield of rational function field $\mathbb{Q}(x)$ under a certain...
The answer as to the surjectivity of $\alpha$ is no. As in algebraic number theory, the simplest way to prove that an element is not a norm is by local considerations. Let us consider
$$
y=\frac{(x^3- …
3
votes
A road map through group cohomology
Chapter 2 of these notes by Milne have been helpful to me.
5
votes
Accepted
First Galois cohomology of Weil restriction of $\mathbb{G}_m$
There is a general argument that is slightly more elementary than what you wrote. By standard properties of Weil restrictions, we have $R(L) = \prod_{\sigma} \mathbb{G}_m(L)$, where the product is tak …
- 4,746
2
votes
reference for (co)homology theories
I learned sheaf cohomology from Claire Voisin's Hodge Theory and Complex Algebraic Geometry I. This is a great book. As its name suggests, it also spends quite some time explaining Dolbeault cohomolog …
- 4,746