Equivariant class group. I: Finite generation of the Picard and the class groups of an invariant subring. (Q288490)

A locally Krull scheme is a scheme which is locally the prime spectrum of a Krull domain. The present paper studies the equivariant class group of a locally Krull scheme with an action of a flat group scheme. These properties are applied in the proof that the class group of an invariant subring is finitely generated. Since a Noetherian normal domain is a Krull domain, a normal scheme of finite type over a field is a typical example of a (quasi-compact quasi-separated) locally Krull scheme. Although a Krull domain is integrally closed, it may not be Noetherian. In this paper, the author also considers non-affine locally Krull schemes and the equivariant version of the theory of class groups over them.