Norms and generalized class groups
Let R be a commutative domain and s an idempotent kernel functor on the category of R-modules. An R-module is s-closed if it is isomorphic to its s-localization. Let (R,s)-mod denote the category of s-closed R-modules and R-homomorphisms. There is a ``tensor product'' in (R,s)-mod obtained by taking the s-localization of the ordinary tensor product. The author defines notions of s-separable and s-étale using the s-tensor product and then defines a norm functor for s-étale extensions. It has the expected properties, and induces the appropriate maps on s-Picard and s- Brauer groups. Since the class group of a Krull domain is an s-Picard group and the reflexive Brauer group is an s-Brauer group, this gives a norm map on those groups also.
scientific article; zbMATH DE number 4069029
scientific article