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

Swan, Richard G.

doi:10.1090/S0002-9939-1988-0954977-0

A simple proof of Gabber’s theorem on projective modules over a localized local ring
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Proc. Amer. Math. Soc. 103 (1988), 1025-1030 Request permission

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.

References

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Cohomologie locale des faisceaux cohérents et théorèmes de Lefschetz locaux et globaux

Classes des corps cyclotomiques

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