Rational cohomology of Witt groups

Abstract

Let k be an algebraically closed field of characteristic p and for each n > 0 let W (n) denote the group of Witt vectors of length n. W (n) is a commutative algebraic group. For reference, see Jacobson [2], Serre [6]. One of the important properties of the Witt groups is the following: Every commutative algebraic k-group whose underlying variety is an affine space is a homomorphic image of products of W (n). We compute the rational cohomology of W (n) for n ≥ 2. H∗(W (n), k) = S((V n−1∗)−1βL#)⊗ E(Rn−1∗L#),