A Mayer-Vietoris sequence in non-linear K-theory

Abstract

1.1. The purpose of this discussion is to provide another link in the K-theory introduced in [8] and subsequently developed in [9], [6] and [51. Given a commutative ring R, this theory is a study of the K-groups KA,(R) arising from the category 9(R) of invertible’ R-algebras, i.e. R-algebras A for which there exists an R-algebra B such that A ORB is isomorphic to some polynomial algebra R[X,, . . . , X,,]. Here (Theorem 9.16) we will show the existence, under certain hypotheses, of the “Mayer-Vietoris sequence”; that is, given a pullback diagram