Reduced Steenrod operations and resolution of singularities

Abstract

We give a new construction of a weak form of Steenrod operations for Chow groups modulo a prime number p for a certain class of varieties. This class contains projective homogeneous varieties which are either split or considered over a field admitting some form of resolution of singularities, for example any field of characteristic not p . These reduced Steenrod operations are sufficient for some applications to the theory of quadratic forms.