Skip to Main content Skip to Navigation
Preprints, Working Papers, ...

Quadratic Pairs on Azumaya Algebras over a Scheme

Abstract : We investigate quadratic pairs for Azumaya algebras with involutions over a base scheme S as defined by Calmès and Fasel, generalizing the case of quadratic pairs on central simple algebras over a field (Knus, Merkurjev, Rost, Tignol). We describe a cohomological obstruction for an Azumaya algebra over S with orthogonal involution to admit a quadratic pair. When S is affine this obstruction vanishes, however it is non-trivial in general. In particular, we construct explicit examples with non-trivial obstructions.
Document type :
Preprints, Working Papers, ...
Complete list of metadata
Contributor : Philippe Gille Connect in order to contact the contributor
Submitted on : Wednesday, September 14, 2022 - 7:54:34 AM
Last modification on : Saturday, September 24, 2022 - 3:36:05 PM


Files produced by the author(s)


  • HAL Id : hal-03776674, version 1
  • ARXIV : 2209.07107


Philippe Gille, Erhard Neher, Cameron Roy Ruether. Quadratic Pairs on Azumaya Algebras over a Scheme. 2022. ⟨hal-03776674⟩



Record views


Files downloads