Linkage of Pfister forms over semi-global fields
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866909336031199232 |
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| author | Daans, Nicolas |
| author_facet | Daans, Nicolas |
| contents | We study linkage of $(d+1)$-fold quadratic Pfister forms over function fields in one variable over a henselian valued field of 2-cohomological dimension $d$. Specifically, we characterise this property in terms of linkage of quadratic Pfister forms over function fields over the residue field of the henselian valued field; in full generality in characteristic different from 2, and for most complete discretely valued fields in characteristic 2. As an application, we obtain a proof that $(d+2)$-fold quadratic Pfister forms over function fields in one variable over a $d$-dimensional higher local field are linked. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_10826 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Linkage of Pfister forms over semi-global fields Daans, Nicolas Number Theory 11E81 (primary), 11E04, 11R58 (secondary) We study linkage of $(d+1)$-fold quadratic Pfister forms over function fields in one variable over a henselian valued field of 2-cohomological dimension $d$. Specifically, we characterise this property in terms of linkage of quadratic Pfister forms over function fields over the residue field of the henselian valued field; in full generality in characteristic different from 2, and for most complete discretely valued fields in characteristic 2. As an application, we obtain a proof that $(d+2)$-fold quadratic Pfister forms over function fields in one variable over a $d$-dimensional higher local field are linked. |
| title | Linkage of Pfister forms over semi-global fields |
| topic | Number Theory 11E81 (primary), 11E04, 11R58 (secondary) |
| url | https://arxiv.org/abs/2402.10826 |