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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

On a question of Quillen


Authors: S. M. Bhatwadekar and R. A. Rao
Journal: Trans. Amer. Math. Soc. 279 (1983), 801-810
MSC: Primary 13C10; Secondary 13H05, 18G05
DOI: https://doi.org/10.1090/S0002-9947-1983-0709584-1
MathSciNet review: 709584
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Abstract: Let $ R$ be a regular local ring, and $ f$ a regular parameter of $ R$. Quillen asked whether every projective $ {R_f}$-module is free. We settle this question when $ R$ is a regular local ring of an affine algebra over a field $ k$. Further, if $ R$ has infinite residue field, we show that projective modules over Laurent polynomial extensions of $ {R_f}$ are also free.


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DOI: https://doi.org/10.1090/S0002-9947-1983-0709584-1
Article copyright: © Copyright 1983 American Mathematical Society