A new proof of the Artin-Springer theorem in Schur index 2
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866914423416815616 |
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| author | Quéguiner-Mathieu, Anne Tignol, Jean-Pierre |
| author_facet | Quéguiner-Mathieu, Anne Tignol, Jean-Pierre |
| contents | We provide a new proof of the analogue of the Artin-Springer theorem for groups of type $\mathsf{D}$ that can be represented by similitudes over an algebra of Schur index $2$: an anisotropic generalized quadratic form over a quaternion algebra $Q$ remains anisotropic after generic splitting of $Q$, hence also under odd degree field extensions of the base field. Our proof is characteristic free and does not use the excellence property. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_16514 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A new proof of the Artin-Springer theorem in Schur index 2 Quéguiner-Mathieu, Anne Tignol, Jean-Pierre K-Theory and Homology 11E39, 14H45 We provide a new proof of the analogue of the Artin-Springer theorem for groups of type $\mathsf{D}$ that can be represented by similitudes over an algebra of Schur index $2$: an anisotropic generalized quadratic form over a quaternion algebra $Q$ remains anisotropic after generic splitting of $Q$, hence also under odd degree field extensions of the base field. Our proof is characteristic free and does not use the excellence property. |
| title | A new proof of the Artin-Springer theorem in Schur index 2 |
| topic | K-Theory and Homology 11E39, 14H45 |
| url | https://arxiv.org/abs/2504.16514 |