Isotropy of orthogonal involutions

Details Isotropy of orthogonal involutions Isotropy of orthogonal involutions

2009-11-21

arxiv.org/abs/0911.4170v3

Mathematics

Algebraic Geometry

13 pages

Scientific paper

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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