2009/11/21 by Nikita A. Karpenko, Karpenko, Nikita A.
Mathematics · #14C25 #14L17 #Advanced Differential Equations and Dynamical Systems #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Commutative Algebra and Its Applications #FOS: Mathematics #Rings and Algebras (math.RA) #math.AG #math.RA #msc:14C25 #msc:14L17
paper · pdf · doi:10.48550/arxiv.0911.4170
13 pages
openalex publication_date 2009/11/21 · arxiv created 2011/03/13 · arxiv updated 2011/03/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.