group cohomology, nonabelian group cohomology, Lie group cohomology
cohomology with constant coefficients / with a local system of coefficients
differential cohomology
Syntomic cohomology is the abelian sheaf cohomology of the syntomic site of a scheme. It is a $p$-adic analogue of Deligne-Beilinson cohomology.
It is closely related to the crystalline cohomology of that scheme. It may be regarded as a $p$-adic absolute Hodge cohomology.
The syntomic site was introduced in
Further developments are in
The following shows that, just as Deligne-Beilinson cohomology may be interpreted as absolute Hodge cohomology, syntomic cohomology may be interpreted as $p$-adic absolute Hodge cohomology.