Isotropy of orthogonal involutions

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.

13 pages

References in corpus (2)

• Quantum Pieri rules for isotropic Grassmannians
• Hyperbolicity of orthogonal involutions

Cited by in corpus (2)

• The J-invariant, Tits algebras and Triality
• Upper motives of algebraic groups and incompressibility of Severi-Brauer varieties