Cohomological dimension at a prime
= Cohomological dimension at a prime
{title2=$\operatorname{cd}_p(K)=\operatorname{cd}_p(G_K)$}
The value $\operatorname{cd}_p(G)$ is the least $n$ such that all cohomology in degrees greater than $n$ vanishes for every discrete $p$-primary torsion module. Vanishing in degree $n+1$ for all such modules suffices by dimension shifting. Dimension does not increase on closed subgroups. For a field, use its <absolute Galois group>.