1 citations
Counting papers with at most 25 authors, so collaboration author lists do not stand in for the people here.
6 papers
Quadratic Spaces and Orthogonal Groups over semilocal Rings
Philippe Gille, Erhard Neher
We prove Springer's Odd Degree Theorem for quadratic forms over LG rings, and Scharlau's and Knebusch's norm principles for quadratic forms over semilocal rings. We present applica…
Non-Stable -Functors of Discrete Valuation Rings Containing a Field
Philippe Gille, Anastasia Stavrova
Let be a field, and let be a simply connected semisimple k-group which is isotropic and contains a strictly proper parabolic -subgroup . Let be a discrete valuati…
Loop torsors. Theory and applications
Philippe Gille, Vladimir Chernousov, Arturo Pianzola
Loop torsors over Laurent polynomial rings in characteristic 0 were originally introduced in relation to infinite dimensional Lie theory. Applications to other areas require a theo…
Group schemes over LG-rings and applications to cancellation theorems and Azumaya algebras
Philippe Gille, Erhard Neher
We prove several results on reductive group schemes over LG-rings, e.g., existence of maximal tori and conjugacy of parabolic subgroups. These were proven in SGA3 for the special c…
Local-global principle for over semiglobal fields
Philippe Gille, Raman Parimala
We compare different local-global principles for torsors under a reductive group G defined over a semiglobal field F. In particular if the F-group G s a retract rational F-variety,…
Loop torsors and Abhyankar's lemma
Philippe Gille
We define the notion of loop torsors under certain group schemes defined over the localization of a regular henselian ring A at a strict normal crossing divisor D. We provide a Gal…