Continuity of total signature maps for Azumaya algebras with involution
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866909913543868416 |
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| author | Astier, Vincent Unger, Thomas |
| author_facet | Astier, Vincent Unger, Thomas |
| contents | In this paper we continue our investigation of signatures of hermitian forms over Azumaya algebras with involution over commutative rings. We show that the approach used in an earlier paper for central simple algebras can be extended to Azumaya algebras and leads to a natural way of choosing the signature of a hermitian form at a given ordering, producing total signatures of hermitian forms that are continuous functions on the real spectrum of the base ring. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_15448 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Continuity of total signature maps for Azumaya algebras with involution Astier, Vincent Unger, Thomas Rings and Algebras 16H05, 11E39, 13J30, 16W10, 06F25 In this paper we continue our investigation of signatures of hermitian forms over Azumaya algebras with involution over commutative rings. We show that the approach used in an earlier paper for central simple algebras can be extended to Azumaya algebras and leads to a natural way of choosing the signature of a hermitian form at a given ordering, producing total signatures of hermitian forms that are continuous functions on the real spectrum of the base ring. |
| title | Continuity of total signature maps for Azumaya algebras with involution |
| topic | Rings and Algebras 16H05, 11E39, 13J30, 16W10, 06F25 |
| url | https://arxiv.org/abs/2511.15448 |