Work

Forms of almost homogeneous varieties over perfect fields

Year: 2024

Type: article

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.

Source: Annales Henri Lebesgue

DOI: 10.5802/ahl.203

Authors: Lucy Moser-Jauslin, Ronan Terpereau

Institutions: Université de Bourgogne, Institut de Mathématiques de Bourgogne, Université de Lille, Laboratoire Paul Painlevé

Language: English

Topic: Algebraic Geometry and Number Theory

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: diamond

Funder: Agence Nationale de la Recherche

Awards: G2659019386, Fibrations and algebraic group actions, G4656594441, Ingénierie et Innovation par les sciences physiques, les savoir-faire technologiques et l'interdisciplinarité, G6803667113