9 citations · 25 across the 14 of their papers we have counts for
17 papers
Flasque resolutions of linear reductive group schemes
Philippe Gille
This paper studies flasque resolutions for linear reductive group schemes over arbitrary bases, extending Colliot-Thelene's theory. A flasque resolution exists for any linear reduc…
When is a reductive group scheme linear?
Philippe Gille
We show that a reductive group scheme over a base scheme S admits a faithful linear representation if and only if its radical torus is isotrivial, that is, it splits after a finite…
Springer's odd degree extension theorem for quadratic forms over semilocal rings
Philippe Gille, Erhard Neher
A fundamental result of Springer says that a quadratic form over a field of characteristic not 2 is isotropic if it is so after an odd degree extension. In this paper we generalize…
Residues on Affine Grassmannians
Mathieu Florence, Philippe Gille
Given a linear group G over a field k, we define a notion of index and residue of an element g of G(k((t)). This provides an alternative proof of Gabber's theorem stating that G ha…
Local triviality for G-torsors
Philippe Gille, Raman Parimala, V. Suresh
Let C Spec(R) be a relative proper flat curve over an henselian base. Let G be a reductive C-group scheme. Under mild technical assumptions, we show that a G-torsor o…
Semi-simple groups that are quasi-split over a tamely-ramified extension
Philippe Gille
Let K be a discretly henselian field whose residue field is separably closed. Answering a question raised by G. Prasad, we show that a semisimple K-- group G is quasi-split if and…