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Comparison of exterior power operations on higher K-theory of schemes

Comparison of exterior power operations on higher K-theory of schemes
Comparison of exterior power operations on higher K-theory of schemes
Exterior power operations provide an additional structure on K-groups of schemes which lies at the heart of Grothendieck's Riemann-Roch theory. Over the past decades, various authors have constructed such operations on higher K-theory. In this paper, we prove that these constructions actually yield the same operations. This leads to the proof of a conjecture by the first author about composition ofthese operations in the equivariant context. As a by-product we make the proof of Grayson's explicit description of higher K-groups accessible to the reader not familiar with the language of spectra.
exterior power operations; higher K-groups; homotopy fibre; Dold-Puppe construction; categories with weak equivalences; lambda ring; equivariant K-theory; Köck's conjecture
2331-8422
Koeck, Bernhard
84d11519-7828-43a6-852b-0c1b80edeef9
Zanchetta, Ferdinando
9bbe0774-d23e-4bf5-95f9-a09fc23d9db7
Koeck, Bernhard
84d11519-7828-43a6-852b-0c1b80edeef9
Zanchetta, Ferdinando
9bbe0774-d23e-4bf5-95f9-a09fc23d9db7

Koeck, Bernhard and Zanchetta, Ferdinando (2021) Comparison of exterior power operations on higher K-theory of schemes. arXiv. (In Press)

Record type: Article

Abstract

Exterior power operations provide an additional structure on K-groups of schemes which lies at the heart of Grothendieck's Riemann-Roch theory. Over the past decades, various authors have constructed such operations on higher K-theory. In this paper, we prove that these constructions actually yield the same operations. This leads to the proof of a conjecture by the first author about composition ofthese operations in the equivariant context. As a by-product we make the proof of Grayson's explicit description of higher K-groups accessible to the reader not familiar with the language of spectra.

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ExteriorPowerComparisonArXivVersion - Accepted Manuscript
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Accepted/In Press date: 13 October 2021
Keywords: exterior power operations; higher K-groups; homotopy fibre; Dold-Puppe construction; categories with weak equivalences; lambda ring; equivariant K-theory; Köck's conjecture

Identifiers

Local EPrints ID: 452484
URI: http://eprints.soton.ac.uk/id/eprint/452484
ISSN: 2331-8422
PURE UUID: f494be37-310c-466b-90b9-e367b1345887
ORCID for Bernhard Koeck: ORCID iD orcid.org/0000-0001-6943-7874

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Date deposited: 11 Dec 2021 11:17
Last modified: 13 Dec 2021 02:49

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Contributors

Author: Bernhard Koeck ORCID iD
Author: Ferdinando Zanchetta

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