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Preprints, Working Papers, ... Year : 2023

Azumaya Algebras and Obstructions to Quadratic Pairs 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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Dates and versions

hal-03776674 , version 1 (14-09-2022)
hal-03776674 , version 2 (12-04-2023)
hal-03776674 , version 3 (07-07-2023)
hal-03776674 , version 4 (21-10-2023)
hal-03776674 , version 5 (15-11-2023)

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Cite

Philippe Gille, Erhard Neher, Cameron Ruether. Azumaya Algebras and Obstructions to Quadratic Pairs over a Scheme. 2023. ⟨hal-03776674v5⟩
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