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research article
Special Reductive Groups Over An Arbitrary Field
A linear algebraic group G defined over a field k is called special if every G-torsor over every field extension of k is trivial. In 1958 Grothendieck classified special groups in the case where the base field is algebraically closed. In this paper we describe the derived subgroup and the coradical of a special reductive group over an arbitrary field k. We also classify special semisimple groups, special reductive groups of inner type, and special quasisplit reductive groups over an arbitrary field k. Finally, we give an application to a conjecture of Serre.
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Type
research article
Web of Science ID
WOS:000387598100007
Authors
Publication date
2016
Publisher
Published in
Volume
21
Issue
4
Start page
1079
End page
1104
Peer reviewed
REVIEWED
EPFL units
Available on Infoscience
January 24, 2017