Cohomological Invariants in Positive Characteristic

Abstract We determine the mod $p$ cohomological invariants for several affine group schemes $G$ in characteristic $p$. These are of $G$-torsors with values étale motivic cohomology, or equivalently Kato’s version Galois cohomology based on differential forms. In particular, we find 2 symmetric groups and orthogonal 2, which Serre computed not 2. also all operations fields, extending Vial’s computation Milnor K-theory fields.