Bayer-Fluckiger, EvaFirst, Uriya A.2017-05-302017-05-302017-05-30201710.1016/j.aim.2017.03.012https://infoscience.epfl.ch/handle/20.500.14299/137872WOS:000400539900005Let 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.Hermitian formMaximal orderHereditary orderRational isomorphismEtale cohomologyReductive groupGroup schemeOrthogonal representationHermitian categoryBruhat-Tits theorytext::journal::journal article::research article