#### Vol. 2, No. 3, 2017

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

### Tom Harris, Bernhard Köck and Lenny Taelman

Vol. 2 (2017), No. 3, 409–450
##### 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.

##### Keywords
exterior power operations, binary complexes, higher algebraic $K$-theory, lambda ring, Dold–Kan correspondence, Dold–Puppe construction, simplicial tensor product, plethysm problem, polynomial functor, Schur algebra
##### Mathematical Subject Classification 2010
Primary: 19D99
Secondary: 13D15, 14F99, 19E08, 20G05