Pré-Publication, Document De Travail Année : 2025

Oriented embedding functors of tori as homogeneous spaces

Résumé

We provide a characterization of homogeneous spaces under a reductive group scheme such that the geometric stabilizers are maximal tori. The quasi-split case over a semilocal base is of special interest and permits to answer a question raised by Marc Levine on homogeneous SL_n-spaces. At the end, we provide an application to the local-global principles for embeddings of étale algebras with involution into central simple algebras with involution.

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Dates et versions

hal-04171950 , version 1 (27-07-2023)
hal-04171950 , version 2 (10-07-2024)
hal-04171950 , version 3 (31-01-2025)

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Philippe Gille, Ting-Yu Lee. Oriented embedding functors of tori as homogeneous spaces. 2025. ⟨hal-04171950v3⟩
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