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Results tagged with cohomology
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user 17907
A branch of algebraic topology concerning the study of cocycles and coboundaries. It is in some sense a dual theory to homology theory. This tag can be further specialized by using it in conjunction with the tags group-cohomology, etale-cohomology, sheaf-cohomology, galois-cohomology, lie-algebra-cohomology, motivic-cohomology, equivariant-cohomology, ...
6
votes
Accepted
Reference request to proof that H$^2(\Gamma, \mathbb{Q}/\mathbb{Z}) = 0$
By the Galois cohomology long exact sequence, this is isomorphic to $\operatorname{H}^3(\Gamma,\mathbb{Z})$, and the vanishing of this is Chapter I, Corollary 4.17 in Milne's Arithmetic Duality Theorems …
- 4,745
2
votes
reference for (co)homology theories
As its name suggests, it also spends quite some time explaining Dolbeault cohomology, De Rham cohomology, singular cohomology, and how all these are defined/can be understood in terms of sheaf cohomology … (There's no group cohomology, as far as I recall.) …
- 4,745
8
votes
Brauer group of projective space
Let $X$ be an $n$-dimensional projective space over a field $k$. Let $k_s$ be a separable closure of $k$, and $X_s$ the base change of $X$ to $k_s$. The algebraic part $\textrm{Br}_1(X)$ of the Brauer …
- 9,497