Submission: 2009, Oct 8
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.
2000 Mathematics Subject Classification: 14C40; 11E04
Keywords and Phrases: Steenrod operations, Riemann-Roch theorem, Chow groups, Witt indices
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