Hensel's lemma for the norm principle for spinor groups
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866915789279330304 |
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| author | Soofiani, Amin |
| author_facet | Soofiani, Amin |
| contents | Let $K$ be a complete discretely valued field with residue field $k$ with $char \ k \ne 2$. Assuming that the norm principle holds for spinor groups $Spin(\mathfrak{h})$ for every regular skew-hermitian form $\mathfrak{h}$ over every quaternion algebra $\mathfrak{D}$ (with respect to the canonical involution on $\mathfrak{D}$) defined over any finite extension of $k$, we show that the norm principle holds for spinor groups $Spin(h)$ for every regular skew-hermitian form $h$ over every quaternion algebra $D$ (with respect to the canonical involution on $D$) defined over $K$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_15737 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Hensel's lemma for the norm principle for spinor groups Soofiani, Amin Group Theory Algebraic Geometry Number Theory Rings and Algebras 20G15 (Primary) 20G10, 14L35, 11E72, 11E39, 11E81, 11E88 (Secondary) Let $K$ be a complete discretely valued field with residue field $k$ with $char \ k \ne 2$. Assuming that the norm principle holds for spinor groups $Spin(\mathfrak{h})$ for every regular skew-hermitian form $\mathfrak{h}$ over every quaternion algebra $\mathfrak{D}$ (with respect to the canonical involution on $\mathfrak{D}$) defined over any finite extension of $k$, we show that the norm principle holds for spinor groups $Spin(h)$ for every regular skew-hermitian form $h$ over every quaternion algebra $D$ (with respect to the canonical involution on $D$) defined over $K$. |
| title | Hensel's lemma for the norm principle for spinor groups |
| topic | Group Theory Algebraic Geometry Number Theory Rings and Algebras 20G15 (Primary) 20G10, 14L35, 11E72, 11E39, 11E81, 11E88 (Secondary) |
| url | https://arxiv.org/abs/2412.15737 |