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arXiv · 2307.16475

Oriented embedding functors of tori as homogeneous spaces

Philippe Gille·Ting-Yu Lee
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Abstract

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 \'etale algebras with involution into central simple algebras with involution.

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Philippe Gille, Ting-Yu Lee. 2023-07-31. Oriented embedding functors of tori as homogeneous spaces. https://arxiv.org/abs/2307.16475

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