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

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 λ-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 λ-ring on one generator.

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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
Received: 20 July 2016
Revised: 5 September 2016
Accepted: 16 October 2016
Published: 1 June 2017
Tom Harris
University Printing House
Shaftesbury Avenue
United Kingdom
Bernhard Köck
Mathematical Sciences
University of Southampton
SO17 1BJ
United Kingdom
Lenny Taelman
Korteweg-de Vries Instituut
Universiteit van Amsterdam
P.O. Box 94248
1090 GE Amsterdam