On the depth of cohomology modules

We study the cohomology modules H-i(G,R) of a p-group G acting on a

ring R of characteristic p, for i>0. In particular, we are interested

in the Cohen-Macaulay property and the depth of H-i(G,R) regarded as an

R-G-module. We first determine the support of H-i(G,R), which turns out

to be independent of i. Then we study the Cohen-Macaulay property for

H-1(G,R). Further results are restricted to the special case that G is

cyclic and R is the symmetric algebra of a vector space on which G

acts. We determine the depth of H-i(G,R) for i odd and obtain results

in certain cases for i even. Along the way, we determine the degrees in

which the transfer map Tr-G R -->R-G has non-zero image.