"Depth of Modular Invariant Rings"
Preprint 1997

Authors: H.E.A. Campbell, I.P. Hughes, G. Kemper, R.J. Shank, D.L. Wehlau

Addresses: Campbell, Hughes, Shank, Wehlau:
             Queen's University, Kingston, Ontario,
           Kemper: Univeritaet Heidelberg,


Abstract:

  It is well known that the ring of invariants associated to a
  non-modular representation of a finite group is Cohen-Macaulay and
  hence has depth equal to the dimension of the representation.  For
  modular representations the ring of invariants usually fails to be
  Cohen-Macaulay and computing the depth is often very difficult.  In
  this paper we obtain a simple formula for the depth of the ring of
  invariants for a family of modular representations. This family
  includes all modular representations of cyclic groups. In
  particular, we obtain an elementary proof of the celebrated theorem
  of Ellingsrud and Skjelbred. We also prove that the ring of
  invariants of a p-group is Cohen-Macaulay if and only if it is
  Buchsbaum.