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Quadratic Pairs on Azumaya Algebras over a Scheme

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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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hal-03776674 , version 1 (14-09-2022)

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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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