A degree bound for rings of arithmetic invariants

Abstract

Consider a Noetherian domain R and a finite group G⊆Gln(R). We prove that if the ring of invariants R[x1,…,xn]G is a Cohen-Macaulay ring, then it is generated as an R-algebra by elements of degree at most max⁡(|G|,n(|G|−1)). As an intermediate result we also show that if R is a Noetherian local ring with infinite residue field then such a ring of invariants of a finite group G over R contains a homogeneous system of parameters consisting of elements of degree at most |G|.