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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 simple proof of Gabber's theorem on projective modules over a localized local ring


Author: Richard G. Swan
Journal: Proc. Amer. Math. Soc. 103 (1988), 1025-1030
MSC: Primary 13C10; Secondary 14F05
MathSciNet review: 954977
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Abstract: Let $ A$ be a regular local ring of dimension 3 and let $ u$ be an element of $ A$ not in the square of the maximal ideal. Gabber has shown that all projective modules over $ A[{u^{ - 1}}]$ are free. An elementary proof of this fact is given here.


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DOI: http://dx.doi.org/10.1090/S0002-9939-1988-0954977-0
PII: S 0002-9939(1988)0954977-0
Article copyright: © Copyright 1988 American Mathematical Society