Arithmetic invariants of pseudoreflection groups and regular graded algebras

Abstract

The main result of this paper is a generalization of the theorem of Chevalley-Shephard-Todd to the rings of invariants of pseudoreflection groups over Dedekind domains. In the special case of a principal ideal domain in which the group order is invertible it is proved that this ring of invariants is isomorphic to a polynomial ring. An intermediate result is that every finitely generated regular graded algebra over a Dedekind domain is isomorphic to a tensor product of blowup algebras.