Depth of modular invariant rings

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 paper1 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 [6].

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