On the depth of separating invariants for finite groups

Abstract. Consider a finite group G acting on a vector space V over a field k of characteristic p > 0. A separating algebra is a subalgebra A of the ring of invariants k[V]^G with the same point separation properties. In this article we compare the depth of an arbitrary separating algebra with that of the corresponding ring of invariants. We show that, in some special cases, the depth of A is bounded above by the depth of k[V]^G