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arXiv · 0911.4170

Isotropy of orthogonal involutions

Nikita A. Karpenko
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Abstract

An orthogonal involution on a central simple algebra becoming isotropic over any splitting field of the algebra, becomes isotropic over a finite odd degree extension of the base field (provided that the characteristic of the base field is not 2). The proof makes use of a structure theorem for Chow motives with finite coefficients of projective homogeneous varieties, of incompressibility of certain generalized Severi-Brauer varieties, and of Steenrod operations.

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Nikita A. Karpenko. 2009-11-21. Isotropy of orthogonal involutions. https://arxiv.org/abs/0911.4170

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