On the structure of flat families of complete homogeneous varieties

Abstract

In this paper, we investigate flat families of complete homogeneous varieties. Over a reduced, noetherian base of characteristic 0, such a family turns out to be a homogeneous space under the natural action of the neutral component of its automorphism group scheme; further, after an étale base change, such a family can be expressed as a product of an abelian scheme and a Borel scheme. The structure of the neutral component of the automorphism group scheme of such a family is also obtained. These results extend already known structure results for complete homogeneous varieties over algebraically closed fields.