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2017 Exterior power operations on higher $K$-groups via binary complexes
Tom Harris, Bernhard Köck, Lenny Taelman
Ann. K-Theory 2(3): 409-450 (2017). DOI: 10.2140/akt.2017.2.409

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 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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Tom Harris. Bernhard Köck. Lenny Taelman. "Exterior power operations on higher $K$-groups via binary complexes." Ann. K-Theory 2 (3) 409 - 450, 2017. https://doi.org/10.2140/akt.2017.2.409

Information

Received: 20 July 2016; Revised: 5 September 2016; Accepted: 16 October 2016; Published: 2017
First available in Project Euclid: 19 October 2017

zbMATH: 1369.19004
MathSciNet: MR3658990
Digital Object Identifier: 10.2140/akt.2017.2.409

Subjects:
Primary: 19D99
Secondary: 13D15 , 14F99 , 19E08 , 20G05

Keywords: binary complexes , Dold–Kan correspondence , Dold–Puppe construction , exterior power operations , higher algebraic $K$-theory , lambda ring , plethysm problem , polynomial functor , Schur algebra , simplicial tensor product

Rights: Copyright © 2017 Mathematical Sciences Publishers

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