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 a scheme.
It is closely related to the crystalline cohomology of that scheme. It may be regarded as an example of an absolute cohomology theory.
The syntomic site was introduced in
Further developments are in