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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

A theorem on smoothness-
Bass-Quillen, Chow groups and
intersection multiplicity of Serre


Author: S. P. Dutta
Journal: Trans. Amer. Math. Soc. 352 (2000), 1635-1645
MSC (1991): Primary 13D02; Secondary 13H10
Published electronically: May 3, 1999
MathSciNet review: 1621737
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Abstract | References | Similar Articles | Additional Information

Abstract: We describe here an inherent connection of smoothness among the Bass-Quillen conjecture, the Chow-group problem and Serre's Theorem on Intersection Multiplicity. Extension of a theorem of Lindel on smoothness plays a key role in our proof of the Serre-multiplicity theorem in the geometric (resp. unramified) case. We reduce the complete case of the theorem to the above case by using Artin's Approximation. We do not need the concept of ``complete Tor''. Similar proofs are sketched for Quillen's theorem on Chow groups and its extension due to Gillet and Levine.


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Additional Information

S. P. Dutta
Affiliation: Department of Mathematics, University of Illinois, 1409 West Green Street, Urbana, Illinois 61801
Email: dutta@math.uiuc.edu

DOI: http://dx.doi.org/10.1090/S0002-9947-99-02372-7
PII: S 0002-9947(99)02372-7
Received by editor(s): September 9, 1997
Published electronically: May 3, 1999
Additional Notes: This research was partially supported by an N.S.A. grant and an N.S.F. grant.
Article copyright: © Copyright 2000 American Mathematical Society