Witt groups of Severi-Brauer varieties and of function fields of conics
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2023
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| _version_ | 1866914603128061952 |
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| author | Quéguiner-Mathieu, Anne Tignol, Jean-Pierre |
| author_facet | Quéguiner-Mathieu, Anne Tignol, Jean-Pierre |
| contents | The Witt group of skew hermitian forms over a division algebra $D$ with symplectic involution is shown to be canonically isomorphic to the Witt group of symmetric bilinear forms over the Severi-Brauer variety of $D$ with values in a suitable line bundle. In the special case where $D$ is a quaternion algebra we extend previous work by Pfister and by Parimala on the Witt group of conics to set up two five-terms exact sequences relating the Witt groups of hermitian or skew-hermitian forms over $D$ with the Witt groups of the center, of the function field of the Severi-Brauer conic of $D$, and of the residue fields at each closed point of the conic. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2304_03539 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Witt groups of Severi-Brauer varieties and of function fields of conics Quéguiner-Mathieu, Anne Tignol, Jean-Pierre K-Theory and Homology 19G12, 11E81, 14H05 The Witt group of skew hermitian forms over a division algebra $D$ with symplectic involution is shown to be canonically isomorphic to the Witt group of symmetric bilinear forms over the Severi-Brauer variety of $D$ with values in a suitable line bundle. In the special case where $D$ is a quaternion algebra we extend previous work by Pfister and by Parimala on the Witt group of conics to set up two five-terms exact sequences relating the Witt groups of hermitian or skew-hermitian forms over $D$ with the Witt groups of the center, of the function field of the Severi-Brauer conic of $D$, and of the residue fields at each closed point of the conic. |
| title | Witt groups of Severi-Brauer varieties and of function fields of conics |
| topic | K-Theory and Homology 19G12, 11E81, 14H05 |
| url | https://arxiv.org/abs/2304.03539 |