The obstruction to excision in K-theory and in cyclic homology

Abstract

Let $f:A\to B$ be a ring homomorphism of not necessarily unital rings and $I◃A$ an ideal 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 $K_{\ast }(A:I)\to K_{\ast }(B:f(I))$ to be an isomorphism; it is measured by the birelative groups $K_{\ast }(A,B:I)$. 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.

Final version to appear in Inventiones

References in corpus (2)

• Excision in bivariant periodic cyclic cohomology: a categorical approach
• Infinitesimal K-theory

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