Hyperbolicity of orthogonal involutions

2009/04/18 by Nikita A. Karpenko, Karpenko, Nikita A. · 3 citations
Mathematics · #14C25 #14L17 #Advanced Algebra and Geometry #Advanced Topics in Algebra #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #math.AG #msc:14C25 #msc:14L17

paper · pdf · doi:10.48550/arxiv.0904.2850

16 pages

arxiv created 2009/04/18 · openalex publication_date 2009/04/18 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We show that a non-hyperbolic orthogonal involution on a central simple algebra over a field of characteristic different from 2 remains non-hyperbolic over some splitting field of the algebra.

Cited by

• Upper motives of algebraic groups and incompressibility of Severi-Brauer\n varieties
• Isotropy of orthogonal involutions
• Rational connectedness for groups of proper projective similitudes

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• On involutions of type \O(\q,k) over a field of\n characteristic two