الملخص الإنجليزي
Abstract:
We prove standard results of group cohomology – namely, existence of a long exact sequence,
classification of torsors via the first cohomology group, Shapiro’s lemma, the Hochschild-
Serre spectral sequence, a decomposition of the cochain complex in the direct product case,
and Jannsen’s result on the recovery problem – for cohomology theories such as continuous,
analytic, bounded, and pro-analytic cohomology. We also prove these results for certain
monoids, as the applications we have in mind concern (ϕ, )-modules. The cohomology
groups considered here all have very concrete interpretations by means of a cochain complex.
Therefore, we do not use methods of homological algebra, but explicit calculations on the
level of cochains, using techniques dating back to Hochschild and Serre
