Pfister's local-global principle for Azumaya algebras with involution
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2022
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| _version_ | 1866915468775784448 |
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| author | Astier, Vincent Unger, Thomas |
| author_facet | Astier, Vincent Unger, Thomas |
| contents | We prove Pfister's local-global principle for hermitian forms over Azumaya algebras with involution over semilocal rings, and show in particular that the Witt group of nonsingular hermitian forms is $2$-primary torsion. Our proof relies on a hermitian version of Sylvester's law of inertia, which is obtained from an investigation of the connections between a pairing of hermitian forms extensively studied by Garrel, signatures of hermitian forms, and positive semidefinite quadratic forms. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2210_04851 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Pfister's local-global principle for Azumaya algebras with involution Astier, Vincent Unger, Thomas Rings and Algebras 16H05, 11E39, 13J30, 16W10 We prove Pfister's local-global principle for hermitian forms over Azumaya algebras with involution over semilocal rings, and show in particular that the Witt group of nonsingular hermitian forms is $2$-primary torsion. Our proof relies on a hermitian version of Sylvester's law of inertia, which is obtained from an investigation of the connections between a pairing of hermitian forms extensively studied by Garrel, signatures of hermitian forms, and positive semidefinite quadratic forms. |
| title | Pfister's local-global principle for Azumaya algebras with involution |
| topic | Rings and Algebras 16H05, 11E39, 13J30, 16W10 |
| url | https://arxiv.org/abs/2210.04851 |