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arXiv · 2504.16514

A new proof of the Artin-Springer theorem in Schur index 2

Anne Quéguiner-Mathieu·Jean-Pierre Tignol
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Abstract

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.

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Anne Quéguiner-Mathieu, Jean-Pierre Tignol. 2025-04-23. A new proof of the Artin-Springer theorem in Schur index 2. https://arxiv.org/abs/2504.16514

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