Given a finite locally free commutative group scheme G over some base scheme S one can consider the corresponding higher classifying stacks B^nG=K(G,n); these are algebro-geometric versions of the corresponding Eilenberg-Maclane spaces. I will talk about how given a reasonable cohomology theory RG_? (e.g. “?” could be structure sheaf cohomology, singular, etale, de Rham, or prismatic cohomology) one can compute the cohomology of K(G,n) in a uniform fashion. More precisely, one can construct a canonical filtration on RG_?(K(G,n)), whose associated graded is the free divided power algebra on D_?(G)[-n], where D_?(G) is a certain 2-term complex which we call the “Dieudonne module” associated to RG_?. Moreover, if multiplication by 2 on RG_? is invertible then this filtration typically splits, giving an explicit formula for RG_?(K(G,n)) as an E_{n-1}-algebra. This is joint work with Shizhang Li and Shubhodip Mondal.