3 papers
math.AG2026
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…
math.AG2025
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…
math.AG2024
The Norm Functor over Schemes
Philippe Gille, Erhard Neher, Cameron Ruether
We construct a globalization of Ferrand's norm functor over rings which generalizes it to the setting of a finite locally free morphism of schemes of constant rank. It sen…