Bass' NK groups and cdh-fibrant Hochschild homology

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The K-theory of a polynomial ring R[t] contains the K-theory of R as a summand. For R commutative and containing ℚ, we describe K*(R[t])/K*(R) in terms of Hochschild homology and the cohomology of Kähler differentials for the cdh topology. We use this to address Bass' question, whether Kn(R)=Kn...

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Autores principales: Cortiñas, G., Haesemeyer, C., Walker, M.E., Weibel, C.
Formato: Artículo publishedVersion
Lenguaje:Inglés
Publicado: 2010
Acceso en línea:http://hdl.handle.net/20.500.12110/paper_00209910_v181_n2_p421_Cortinas
Aporte de:
Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires
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spelling paperaa:paper_00209910_v181_n2_p421_Cortinas2023-06-12T16:42:17Z Bass' NK groups and cdh-fibrant Hochschild homology Invent. Math. 2010;181(2):421-448 Cortiñas, G. Haesemeyer, C. Walker, M.E. Weibel, C. The K-theory of a polynomial ring R[t] contains the K-theory of R as a summand. For R commutative and containing ℚ, we describe K*(R[t])/K*(R) in terms of Hochschild homology and the cohomology of Kähler differentials for the cdh topology. We use this to address Bass' question, whether Kn(R)=Kn(R[t]) implies Kn(R)=Kn(R[t1,t2]). The answer to this question is affirmative when R is essentially of finite type over the complex numbers, but negative in general. © 2010 The Author(s). Fil:Cortiñas, G. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. 2010 info:eu-repo/semantics/article info:ar-repo/semantics/artículo info:eu-repo/semantics/publishedVersion application/pdf eng info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar http://hdl.handle.net/20.500.12110/paper_00209910_v181_n2_p421_Cortinas
institution Universidad de Buenos Aires
institution_str I-28
repository_str R-134
collection Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA)
language Inglés
orig_language_str_mv eng
description The K-theory of a polynomial ring R[t] contains the K-theory of R as a summand. For R commutative and containing ℚ, we describe K*(R[t])/K*(R) in terms of Hochschild homology and the cohomology of Kähler differentials for the cdh topology. We use this to address Bass' question, whether Kn(R)=Kn(R[t]) implies Kn(R)=Kn(R[t1,t2]). The answer to this question is affirmative when R is essentially of finite type over the complex numbers, but negative in general. © 2010 The Author(s).
format Artículo
Artículo
publishedVersion
author Cortiñas, G.
Haesemeyer, C.
Walker, M.E.
Weibel, C.
spellingShingle Cortiñas, G.
Haesemeyer, C.
Walker, M.E.
Weibel, C.
Bass' NK groups and cdh-fibrant Hochschild homology
author_facet Cortiñas, G.
Haesemeyer, C.
Walker, M.E.
Weibel, C.
author_sort Cortiñas, G.
title Bass' NK groups and cdh-fibrant Hochschild homology
title_short Bass' NK groups and cdh-fibrant Hochschild homology
title_full Bass' NK groups and cdh-fibrant Hochschild homology
title_fullStr Bass' NK groups and cdh-fibrant Hochschild homology
title_full_unstemmed Bass' NK groups and cdh-fibrant Hochschild homology
title_sort bass' nk groups and cdh-fibrant hochschild homology
publishDate 2010
url http://hdl.handle.net/20.500.12110/paper_00209910_v181_n2_p421_Cortinas
work_keys_str_mv AT cortinasg bassnkgroupsandcdhfibranthochschildhomology
AT haesemeyerc bassnkgroupsandcdhfibranthochschildhomology
AT walkerme bassnkgroupsandcdhfibranthochschildhomology
AT weibelc bassnkgroupsandcdhfibranthochschildhomology
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