Azumaya Algebras and Obstructions to Quadratic Pairs over a Scheme
Fuente:
arXiv
Gespeichert in:
| Hauptverfasser: | , , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2022
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866912205799161856 |
|---|---|
| author | Gille, Philippe Neher, Erhard Ruether, Cameron |
| author_facet | Gille, Philippe Neher, Erhard Ruether, Cameron |
| contents | We investigate quadratic pairs for Azumaya algebras with involutions over a base scheme S as defined by Calm{è}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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2209_07107 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Azumaya Algebras and Obstructions to Quadratic Pairs over a Scheme Gille, Philippe Neher, Erhard Ruether, Cameron Algebraic Geometry Rings and Algebras We investigate quadratic pairs for Azumaya algebras with involutions over a base scheme S as defined by Calm{è}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. |
| title | Azumaya Algebras and Obstructions to Quadratic Pairs over a Scheme |
| topic | Algebraic Geometry Rings and Algebras |
| url | https://arxiv.org/abs/2209.07107 |