UCLA

Using the recent work of Frankland and Spitzweck, we define motivic Steenrod operations

on the mod p motivic cohomology of smooth varieties defined over a base field of characteristic

p. We show that the operations satisfy expected properties such as the Adem relations and

Cartan formula when restricted to mod p Chow groups. Using these new operations, we remove previous

restrictions on the characteristic of the base field for Rost's degree formula. We also prove

Hoffmann's conjecture (generalized to include quadratic forms over a base field of characteristic

2) on the possible values of the first Witt index of an anisotropic quadratic form for the special

case of nonsingular anisotropic quadratic forms over a base field of characteristic 2.