Geodesic
A short proof of a theorem due to O. Gabber
Zapiski Nauchnykh Seminarov POMI, Algebra and number theory. Part 2, Tome 479 (2019), pp. 131-136 Cet article a éte moissonné depuis la source Math-Net.Ru

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A very short proof of an unpublished result due to O. Gabber is given. More presicely, let $R$ be a regular local ring, containing a finite field $k$. Let $\mathbf{G}$ be a simply-connected reductive group scheme over $k$. We prove that a principal $\mathbf{G}$-bundle over $R$ is trivial, if it is trivial over the fraction field of $R$. This is the mentioned unpublished result due to O. Gabber. We derive this result from a purely geometric one proven in another paper of the author and stated in the Introduction. 
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     title = {A short proof of a theorem due to {O.~Gabber}},
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I. A. Panin. A short proof of a theorem due to O. Gabber. Zapiski Nauchnykh Seminarov POMI, Algebra and number theory. Part 2, Tome 479 (2019), pp. 131-136. http://geodesic.mathdoc.fr/item/ZNSL_2019_479_a5/

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