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Isotropy of orthogonal involutions
- American Journal of Mathematics
- Johns Hopkins University Press
- Volume 135, Number 1, February 2013
- pp. 1-15
- 10.1353/ajm.2013.0011
- Article
- Additional Information
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.