Essential dimension of sequences of quadratic Pfister forms
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866908610670362624 |
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| author | Bingöl, Fatma Kader Chapman, Adam Laghribi, Ahmed |
| author_facet | Bingöl, Fatma Kader Chapman, Adam Laghribi, Ahmed |
| contents | We study the essential dimension of the set of isometry classes of $m$-tuples $(φ_1,...,φ_m)$ of quadratic $n$-fold Pfister forms over a field $F$ such that the Witt class of $φ_1 \perp \ldots \perp φ_m$ lies in $I_q^{n+1}F$. We show that the essential dimension is equal to $n+1$, when $m=3$, and is either $4$ or $5$, when $n=\text{char} F=2$, $m=4$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_22237 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Essential dimension of sequences of quadratic Pfister forms Bingöl, Fatma Kader Chapman, Adam Laghribi, Ahmed Number Theory 11E04, 16K20 We study the essential dimension of the set of isometry classes of $m$-tuples $(φ_1,...,φ_m)$ of quadratic $n$-fold Pfister forms over a field $F$ such that the Witt class of $φ_1 \perp \ldots \perp φ_m$ lies in $I_q^{n+1}F$. We show that the essential dimension is equal to $n+1$, when $m=3$, and is either $4$ or $5$, when $n=\text{char} F=2$, $m=4$. |
| title | Essential dimension of sequences of quadratic Pfister forms |
| topic | Number Theory 11E04, 16K20 |
| url | https://arxiv.org/abs/2505.22237 |