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On the first Steenrod square for Chow groups
- American Journal of Mathematics
- Johns Hopkins University Press
- Volume 135, Number 1, February 2013
- pp. 53-63
- 10.1353/ajm.2013.0003
- Article
- Additional Information
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We construct a weak version of the homological first Steenrod square, a natural transformation
from the modulo two Chow group to the Chow group modulo two and two-torsion. No assumption is
made on the characteristic of the base field. As an application, we generalize a theorem of Nikita
Karpenko on the parity of the first Witt index of quadratic forms to the case of a base field of
characteristic two.