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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.
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Preprints, Working Papers, ...
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https://hal-cnrs.archives-ouvertes.fr/hal-03776674
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

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

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

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