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On the Grothendieck–Serre Conjecture Concerning Principal G-Bundles Over Semilocal Dedekind Domains
- Source :
- Journal of Mathematical Sciences. 222:453-462
- Publication Year :
- 2017
- Publisher :
- Springer Science and Business Media LLC, 2017.
-
Abstract
- Let R be a semilocal Dedekind domain, and let K be the field of fractions of R. Let G be a reductive semisimple simply connected R-group scheme such that every semisimple normal R-subgroup scheme of G contains a split R-torus $$ {\mathbb{G}}_{m,R} $$ . It is proved that the kernel of the map $$ {H}_{\overset{\prime }{e}t}^1\left(R,\kern0.5em G\right)\to {H}_{\overset{\prime }{e}t}^1\left(K,\kern0.5em G\right) $$ induced by the inclusion of R into K is trivial. This result partially extends the Nisnevich theorem.
- Subjects :
- Statistics and Probability
Conjecture
Applied Mathematics
General Mathematics
010102 general mathematics
Field of fractions
Dedekind domain
01 natural sciences
Prime (order theory)
Combinatorics
Kernel (algebra)
Scheme (mathematics)
0103 physical sciences
Simply connected space
Dedekind cut
010307 mathematical physics
0101 mathematics
Mathematics
Subjects
Details
- ISSN :
- 15738795 and 10723374
- Volume :
- 222
- Database :
- OpenAIRE
- Journal :
- Journal of Mathematical Sciences
- Accession number :
- edsair.doi...........052736cfa98a1e9ac787cd74e08c4a1d