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A Short Proof of a Theorem Due to O. Gabber
- Source :
- Journal of Mathematical Sciences. 249:85-88
- Publication Year :
- 2020
- Publisher :
- Springer Science and Business Media LLC, 2020.
-
Abstract
- A very short proof of an unpublished result due to O. Gabber is given. More exactly, let R be a regular local ring containing a finite field k. Let G be a simply-connected reductive group scheme over k. It is proved that a principal G-bundle over R is trivial if it is trivial over the fraction field of R. This is the mentioned unpublished result due to O. Gabber. In this paper, this result is derived from a purely geometric one, proved in another paper of the author and stated in the Introduction.
- Subjects :
- Statistics and Probability
Pure mathematics
Applied Mathematics
General Mathematics
010102 general mathematics
Field (mathematics)
Regular local ring
Reductive group
01 natural sciences
010305 fluids & plasmas
Finite field
Scheme (mathematics)
0103 physical sciences
Fraction (mathematics)
0101 mathematics
Mathematics
Subjects
Details
- ISSN :
- 15738795 and 10723374
- Volume :
- 249
- Database :
- OpenAIRE
- Journal :
- Journal of Mathematical Sciences
- Accession number :
- edsair.doi...........e651761eb733951777b716110fb46891