### On the first Steenrod square for Chow groups, by Olivier Haution

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.

Olivier Haution <olivier.haution(at)gmail.com>