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.
The syntomic site was introduced in
Further developments are in