The ring of reciprocal polynomials and rank varieties

Let p be a prime and let G be a finite p ‐group. In a recent paper we introduced a commutative graded ℤ‐algebra R G (which classifies the so‐called convolutions on G ). Now let K be an algebraically closed field of characteristic p and let M be a non‐zero finitely generated K [ G ]‐module. A general rank variety W G ( M ) is constructed quite explicitly as a determinantal subvariety of the variety of K ‐valued points of the spectrum of R G . Further, it is shown that the quotient variety W G ( M )/ G is inseparably isogenous to the usual cohomological support variety V G ( M ).