A degree bound for rings of arithmetic invariants.

Consider a Noetherian domain R and a finite group G ⊆ G l n (R). We prove that if the ring of invariants R [ x 1 , ... , x n ] 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 |. [ABSTRACT FROM AUTHOR]