Witt invariants of quaternionic forms
Fuente:
arXiv
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866910916121985024 |
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| author | Garrel, Nicolas |
| author_facet | Garrel, Nicolas |
| contents | We describe all Witt invariants of anti-hermitian forms over a quaternion algebra with its canonical involution, and in particular all Witt invariants of orthogonal groups $O(A,σ)$ where $(A,σ)$ is an central simple algebra with orthogonal involution and $A$ has index $2$. They are combinations of appropriately defined $λ$-powers, similarly to the case of quadratic forms, but the module of invariants is no longer free over those operations. The method involves extending the scalars to a generic splitting field of $A$, and controlling the residues of the invariants with respect to valuations coming from closed points in the Severi-Brauer variety. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_08920 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Witt invariants of quaternionic forms Garrel, Nicolas Rings and Algebras 11E81, 16W70, 12G05 We describe all Witt invariants of anti-hermitian forms over a quaternion algebra with its canonical involution, and in particular all Witt invariants of orthogonal groups $O(A,σ)$ where $(A,σ)$ is an central simple algebra with orthogonal involution and $A$ has index $2$. They are combinations of appropriately defined $λ$-powers, similarly to the case of quadratic forms, but the module of invariants is no longer free over those operations. The method involves extending the scalars to a generic splitting field of $A$, and controlling the residues of the invariants with respect to valuations coming from closed points in the Severi-Brauer variety. |
| title | Witt invariants of quaternionic forms |
| topic | Rings and Algebras 11E81, 16W70, 12G05 |
| url | https://arxiv.org/abs/2504.08920 |