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.
Haution, O. (2013). On the first Steenrod square for Chow groups. AMERICAN JOURNAL OF MATHEMATICS, 135(1), 53-63 [10.1353/ajm.2013.0003].
On the first Steenrod square for Chow groups
Haution, O
2013
Abstract
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.
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