Rationally isomorphic hermitian forms and torsors of some non-reductive groups

Let R be a semilocal Dedekind domain. Under certain assumptions, we show that two (not necessarily unimodular) hermitian forms over an R-algebra with involution, which are rationally isomorphic and have isomorphic semisimple coradicals, are in fact isomorphic. The same result is also obtained for quadratic forms equipped with an action of a finite group. The results have cohomological restatements that resemble the Grothendieck-Serre conjecture, except the group schemes involved are not reductive. We show that these group schemes are closely related to group schemes arising in Bruhat-Tits theory. (C) 2017 Elsevier Inc. All rights reserved.


Published in:
Advances In Mathematics, 312, 150-184
Year:
2017
Publisher:
San Diego, Academic Press Inc Elsevier Science
ISSN:
0001-8708
Keywords:
Laboratories:




 Record created 2017-05-30, last modified 2018-03-17


Rate this document:

Rate this document:
1
2
3
 
(Not yet reviewed)