Invariant for Sets of Pfister Forms
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866910392368758784 |
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| author | Chapman, Adam Levin, Ilan |
| author_facet | Chapman, Adam Levin, Ilan |
| contents | We associate an $(n_1+\dots+n_t-k(t-1))$-fold Pfister form to any $t$-tuple of $k$-linked Pfister forms of dimensions $2^{n_1},\dots,2^{n_t}$, and prove its invariance under the different symbol presentations of the forms with a common $k$-fold sub-symbol. We then show that it vanishes when the forms are actually $(k+1)$-linked or when the characteristic is 2 and the forms are inseparably $k$-linked. We study whether the converse statements hold or not. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_00121 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Invariant for Sets of Pfister Forms Chapman, Adam Levin, Ilan K-Theory and Homology Number Theory Primary 19D45, Secondary 11E04, 11E81, 13A35, 16K20 20G10 We associate an $(n_1+\dots+n_t-k(t-1))$-fold Pfister form to any $t$-tuple of $k$-linked Pfister forms of dimensions $2^{n_1},\dots,2^{n_t}$, and prove its invariance under the different symbol presentations of the forms with a common $k$-fold sub-symbol. We then show that it vanishes when the forms are actually $(k+1)$-linked or when the characteristic is 2 and the forms are inseparably $k$-linked. We study whether the converse statements hold or not. |
| title | Invariant for Sets of Pfister Forms |
| topic | K-Theory and Homology Number Theory Primary 19D45, Secondary 11E04, 11E81, 13A35, 16K20 20G10 |
| url | https://arxiv.org/abs/2404.00121 |