The real spectrum of an ideal and KO-theory exact sequences
In [Rocky Mountain J. Math. 14, 733--765 (1984; Zbl 0576.14024)], the author proved that, up to 2-torsion, the Witt ring of any ring A agrees with the ring KO(Sper(A)), where Sper(A) is the real spectrum of A. In the present paper the investigation of the K-theory of real spectra is continued. The main objective is a discussion of the analogues to certain short and long exact sequences in topological \(K\)-theory. In the real spectrum version of these sequences the ringed space structure of real spectra plays an important role. Correspondingly the major part of the paper is dedicated to a study of real spectra as ringed space, in particular of quotients of real spectra by closed subspaces.
scientific article; zbMATH DE number 4025590