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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

A negative answer to a question of Bass


Authors: G. Cortiñas, C. Haesemeyer, Mark E. Walker and C. Weibel
Journal: Proc. Amer. Math. Soc. 139 (2011), 1187-1200
MSC (2010): Primary 19A49, 19D50; Secondary 19D55, 14F20
Published electronically: November 2, 2010
MathSciNet review: 2748413
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Abstract: We address Bass' question, on whether $ K_n(R)=K_n(R[t])$ implies $ K_n(R)=K_n(R[t_1,t_2])$. In a companion paper, we establish a positive answer to this question when $ R$ is of finite type over a field of infinite transcendence degree over the rationals. Here we provide an example of an isolated surface singularity over a number field for which the answer the Bass' question is ``no'' when $ n=0$.


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Additional Information

G. Cortiñas
Affiliation: Departamento Matemática, FCEyN-Universidad de Buenos Aires, Ciudad Universitaria Pab 1, 1428 Buenos Aires, Argentina
Email: gcorti@dm.uba.ar

C. Haesemeyer
Affiliation: Department of Mathematics, University of California, Los Angeles, California 90095
Email: chh@math.ucla.edu

Mark E. Walker
Affiliation: Department of Mathematics, University of Nebraska, Lincoln, Lincoln, Nebraska 68588
Email: mwalker5@math.unl.edu

C. Weibel
Affiliation: Department of Mathematics, Rutgers University, New Brunswick, New Jersey 08901
Email: weibel@math.rutgers.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-2010-10728-1
PII: S 0002-9939(2010)10728-1
Received by editor(s): April 18, 2010
Published electronically: November 2, 2010
Additional Notes: The first author’s research was supported by CONICET and partially supported by grants PICT 2006-00836, UBACyT X051, PIP 112-200801-00900, and MTM2007-64704 (Feder funds).
The second author’s research was partially supported by NSF grant DMS-0652860
The third author’s research was partially supported by NSF grant DMS-0601666.
The fourth author’s research was supported by NSA grant MSPF-04G-184 and the Oswald Veblen Fund.
Communicated by: Irena Peeva
Article copyright: © Copyright 2010 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.