Exterior power operations on higher K-groups via binary complexes

2016/07/31 by Tom Harris, Bernhard Köck, Lenny Taelman · 2 citations
Mathematics · #math.KT #math.AG #math.RT #msc:13D15 #msc:14F99 #msc:19D99 #msc:19E08 #msc:20G05

paper · pdf · doi:10.2140/akt.2017.2.409

published as Ann. K-Th. 2 (2017) 409-450 · 35 pages; v2: reference to a correspondence between Deligne and Grothendieck added; v3: referee's comments incorporated, to appear in Annals of K-Theory

arxiv created 2016/10/18 · arxiv updated 2017/06/14

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 λ-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 λ-ring on one generator.

Cited by

• Exterior power operations on relative K-theory
• On presentations of K-groups by generators and relations

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