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

TL;DR

This paper introduces a new construction of exterior power operations on higher algebraic K-groups using binary multicomplexes, demonstrating they form a λ-ring with key algebraic properties.

Contribution

It provides a novel approach to define exterior power operations on higher K-groups via Grayson's binary multicomplexes, establishing their λ-ring structure.

Findings

Exterior power operations satisfy λ-ring axioms

Operations adhere to product and composition laws

Grothendieck group of polynomial functors is universal λ-ring

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 (quasi-compact) scheme. We show that these operations satisfy the axioms of a $\lambda$-ring, including the product and composition laws. To prove the composition law we show that the Grothendieck group of the exact category of integral polynomial functors is the universal $\lambda$-ring on one generator.