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arXiv · 2209.07107

Azumaya Algebras and Obstructions to Quadratic Pairs over a Scheme

Philippe Gille·Erhard Neher·Cameron Ruether
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Abstract

We investigate quadratic pairs for Azumaya algebras with involutions over a base scheme S as defined by Calm{\`e}s 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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Philippe Gille, Erhard Neher, Cameron Ruether. 2022-09-15. Azumaya Algebras and Obstructions to Quadratic Pairs over a Scheme. https://arxiv.org/abs/2209.07107

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