The obstruction to excision in K-theory and in cyclic homology, by Guillermo Cortiñas

Let f : A --> B be a ring homomorphism of not necessarily unital rings and I an ideal of A which is mapped by f isomorphically to an ideal of B. The obstruction to excision in K-theory is the failure of the map between relative K-groups K_*(A:I) --> K_*(B:f(I)) to be an isomorphism; it is measured by the birelative groups K_*(A,B:I). We show that these are rationally isomorphic to the corresponding birelative groups for cyclic homology up to a dimension shift. In the particular case when A and B are Q-algebras we obtain an integral isomorphism.

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