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

By Guillermo Cortiñas. 2001

64 citations recorded by the source corpus.

Let f:A→B be a ring homomorphism of not necessarily unital rings and $I\triangleleft{A}$ 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*(A:I)→K*(B:f(I)) to be an isomorphism; it is measured by the birelative groups K*(A,B:I). Similarly the groups HN*(A,B:I) measure the obstruction to excision in negative cyclic homology. We show that the rational Jones-Goodwillie Chern character induces an isomorphism $$ch_{*}:K_{*}(A,B:I)\otimes\mathbb{Q}\overset{\sim}{\to}HN_{*}(A\otimes\mathbb{Q},B\otimes\mathbb{Q}:I\otimes\mathbb{Q}).$$

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/84510c488f6fbaf64010adad3c936ac0f20d2dce

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In Geometry and Topology

In Mathematical Physics

Citations in the corpus

The arc-topology (2018, background): “The question of excision has played a crucial role in algebraic K-theory, see for instance [46, 10, 19].”
The Local Structure of Algebraic K-Theory (2012, unknown): “General excision for closed embeddings is covered rationally by Cortiñas in [57].”
Bi-relative algebraic K-theory and topological cyclic homology (2004, background): “N T ] 1 2 M ar 2 00 6 B i-relative algebraic K -theory and topologicalcyclic hom ology Thom asG eisserand LarsHesselholt Introduction It is well-known that algebraic K -theory preserves products ofrings.”
Cyclic homology, cdh-cohomology and negative K-theory (2005, methodology): “The following theorem was proven by Cortiñas in [5].”