Continuous cohomology of a profinite group
= Continuous cohomology of a profinite group
{title2=$H^q_{\mathrm{cont}}(G,M)$}
For a <profinite group> and a discrete module with continuous action, continuous cohomology is computed by continuous cochains. On a compact domain these cochains have finite image. Positive-degree classes become zero on a sufficiently small open subgroup and hence are torsion by restriction followed by corestriction.