Exterior power operations on higher $K$-groups via binary complexes

Abstract

We use Grayson’s binary multicomplex presentation of algebraic $K$-theory to give a new construction of exterior power operations on the higher $K$-groups of a (quasicompact) scheme. We show that these operations satisfy the axioms of a $\lambda$-ring, including the product and composition laws. To prove the latter we show that the Grothendieck group of the exact category of integral polynomial functors is the universal $\lambda$-ring on one generator.