Bass' NK groups and cdh-fibrant Hochschild homology
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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2010
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| Acceso en línea: | https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00209910_v181_n2_p421_Cortinas http://hdl.handle.net/20.500.12110/paper_00209910_v181_n2_p421_Cortinas |
| Aporte de: |
| Sumario: | 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). |
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