Forms of almost homogeneous varieties over perfect fields
Annales Henri Lebesgue, Volume 7 (2024), pp. 357-407.

Metadata

Keywords Homogeneous space, equivariant embedding, Luna-Vust theory, Galois descent, real structure, real form

Abstract

We study the k-forms of almost homogeneous varieties over perfect base fields k. First, we discuss criteria for the existence of k-forms in the homogeneous case. Then, we extend the Luna-Vust theory from algebraically closed fields to perfect fields to determine when a given k-form of the open orbit of an almost homogeneous variety extends to a k-form of the entire variety. Finally, in the last section, we apply these results to determine the real forms of complex almost homogeneous SL 2 -threefolds.


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