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

Let f: A → 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 *(A:I)→K *(B:f(I)) to be an isomorphism; it is measured by the bire...

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Autor principal: Cortiñas, G.
Formato: JOUR
Acceso en línea:http://hdl.handle.net/20.500.12110/paper_00209910_v164_n1_p143_Cortinas
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Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires
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spelling todo:paper_00209910_v164_n1_p143_Cortinas2023-10-03T14:20:42Z The obstruction to excision in K-theory and in cyclic homology Cortiñas, G. Let f: A → 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 *(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)⊗ ℚ →simHN * A ⊗ℚ,B ⊗ℚ:I ⊗ℚ. JOUR info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar http://hdl.handle.net/20.500.12110/paper_00209910_v164_n1_p143_Cortinas
institution Universidad de Buenos Aires
institution_str I-28
repository_str R-134
collection Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA)
description Let f: A → 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 *(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)⊗ ℚ →simHN * A ⊗ℚ,B ⊗ℚ:I ⊗ℚ.
format JOUR
author Cortiñas, G.
spellingShingle Cortiñas, G.
The obstruction to excision in K-theory and in cyclic homology
author_facet Cortiñas, G.
author_sort Cortiñas, G.
title The obstruction to excision in K-theory and in cyclic homology
title_short The obstruction to excision in K-theory and in cyclic homology
title_full The obstruction to excision in K-theory and in cyclic homology
title_fullStr The obstruction to excision in K-theory and in cyclic homology
title_full_unstemmed The obstruction to excision in K-theory and in cyclic homology
title_sort obstruction to excision in k-theory and in cyclic homology
url http://hdl.handle.net/20.500.12110/paper_00209910_v164_n1_p143_Cortinas
work_keys_str_mv AT cortinasg theobstructiontoexcisioninktheoryandincyclichomology
AT cortinasg obstructiontoexcisioninktheoryandincyclichomology
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