olivier.haution@gmail.com

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

Full text: dvi.gz 22 k, dvi 65 k, ps.gz 773 k, pdf.gz 130 k, pdf 164 k.