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Exterior power operations on higher K-groups via binary complexes

Exterior power operations on higher K-groups via binary complexes
Exterior power operations on higher K-groups via binary complexes
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.
409-450
Harris, Thomas
f030d37f-b4bf-4adc-bc7a-b05afe3a1655
Kock, Bernhard
84d11519-7828-43a6-852b-0c1b80edeef9
Taelman, Lenny
22bf7dc2-6a1a-4d87-983e-16c71a61ef03
Harris, Thomas
f030d37f-b4bf-4adc-bc7a-b05afe3a1655
Kock, Bernhard
84d11519-7828-43a6-852b-0c1b80edeef9
Taelman, Lenny
22bf7dc2-6a1a-4d87-983e-16c71a61ef03

Harris, Thomas, Kock, Bernhard and Taelman, Lenny (2017) Exterior power operations on higher K-groups via binary complexes. Annals of K-Theory, 2 (3), 409-450. (doi:10.2140/akt.2017.2.409).

Record type: Article

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.

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Submitted date: 20 July 2016
Accepted/In Press date: 16 October 2016
e-pub ahead of print date: 1 June 2017
Organisations: Pure Mathematics

Identifiers

Local EPrints ID: 397859
URI: http://eprints.soton.ac.uk/id/eprint/397859
PURE UUID: 0b5447e7-58cd-4370-a584-8c10b68c2bff
ORCID for Bernhard Kock: ORCID iD orcid.org/0000-0001-6943-7874

Catalogue record

Date deposited: 08 Jul 2016 09:16
Last modified: 31 Jan 2020 01:27

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