Some results on the lower K-theory of singular affine varieties
The author gives sufficient conditions for the construction of nonzero elements of the lower algebraic K-theory, \(N^ iK_{-j}(A)\) where A is a singular coordinate ring. For low values of j this sort of calculation has been made in many cases by means of the conductor/normalisation Cartesian square of J. Milnor and its attendant exact sequence. When A is higher-dimensional this method will not work since normalisations need not be regular (A might be its own normalisation). The author circumvents these difficulties by introducing suitable rings which, while not geometric in origin, have Mayer-Vietoris sequences and computable lower K-groups. He then lifts some of the elements which he obtains in this manner.
nonzero elements of the lower algebraic K-theory
scientific article; zbMATH DE number 4000094