Projective modules equipped with a metric over the rings of integers of number fields. (Modules projectifs munis d’une métrique sur les anneaux d’entiers de corps de nombres.) (French) Zbl 0905.19002

Grayson, Daniel R.

C. R. Acad. Sci., Paris, Sér. I 309, No. 9, 573-575 (1989).

Summary: We show that the spectrum of a number ring, when compactified by equipping its projective modules with metrics, still behaves like a Dedekind domain as far as its Grothendieck group is concerned.

MSC:

19A31	\(K_0\) of group rings and orders
11R70	\(K\)-theory of global fields
13F05	Dedekind, Prüfer, Krull and Mori rings and their generalizations
14C22	Picard groups

Keywords:

spectrum of number ring; projective modules; metrics; Dedekind domain; Grothendieck group