6 papers
Oriented embedding functors of tori as homogeneous spaces
Philippe Gille, Ting-Yu Lee
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…
A local-global principle for twisted flag varieties
Philippe Gille, Raman Parimala
We prove a local-global principle for twisted flag varieties over a semiglobal field.
Loop group schemes and Abhyankar's lemma
Philippe Gille
We define the notion of reductive group schemes defined over the localization of a regular henselian ring A at a strict normal crossing divisor . We provide a criterion for the…
Unipotent Subgroups of Stabilizers
Phillipe Gille, Robert Guralnick
We consider semi-continuity of certain dimensions on group schemes.
Azumaya Algebras and Obstructions to Quadratic Pairs over a Scheme
Philippe Gille, Erhard Neher, Cameron Ruether
We investigate quadratic pairs for Azumaya algebras with involutions over a base scheme S as defined by Calm{è}s and Fasel, generalizing the case of quadratic pairs on central simp…
R-equivalence on group schemes
Philippe Gille, A Stavrova
We define R-equivalence for group schemes over a semilocal ring and relate this with rational properties. Two main cases are investigated: tori and isotropic semisimple simply conn…