On a question of Quillen

Bhatwadekar, S. M.; Rao, R. A.

doi:10.1090/S0002-9947-1983-0709584-1

On a question of Quillen
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by S. M. Bhatwadekar and R. A. Rao PDF

Trans. Amer. Math. Soc. 279 (1983), 801-810 Request permission

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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Projective modules over a polynomial ring are free

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