All Questions

What is the cohomological dimension of algebraic number fields like $\Bbb{Q}$, $\Bbb{Q}[i]$, $\Bbb{Q}[\sqrt{3}]$ or similar? I'm interested in computing the cohomological dimension of $\Bbb{A}^1_k$ ...

Let $D$ be the ring of integers of a number field $F$. Let $X=\mathrm{Spec} ~D$, and let $\pi$ be the etale fundamental group of $X$. There are natural maps from $H^i(\pi, \mathbf{Z}/n)$ to $H^i_{...

Concerning http://swc.math.arizona.edu/aws/1999/99RubinES.pdf, especially section I.5: Can one define the Selmer groups and the unramified cohomology groups as étale cohomology groups of certain ...

Let $F/K$ be a Galois extension of number fields with Galois group $G$. Let $\mathcal{O}_F$ and $\mathcal{O}_K$ be the associated rings of integers, and let $n\geq 1$. When is $$ K_{2n-1}(\...

In the paper of Bloch and Kato in the Grothendieck Festschrift, and some other papers relating to the Bloch-Kato conjecture and the ETNC, the cohomology groups $H^i_{\mathrm{et}}(\operatorname{Spec} ...

What are cases when Galois cohomology groups are given by étale cohomology? Example: $S = Spec(K)$ the spectrum of a field, $F \in Sh(K)$, then $H^p(K, F) = H^p(G_K, F_{\bar{K}})$. What if $G = \...