The University of Southampton
University of Southampton Institutional Repository

# Two formulae for exterior power operations on higher K-groups

Harris, Thomas and Koeck, Bernhard (2019) Two formulae for exterior power operations on higher K-groups. Journal of Pure and Applied Algebra, 223, 4925-4936.

Record type: Article

## Abstract

Exterior power operations on the higher K-groups of a quasi-compact scheme have recently been constructed by Taelman and the authors by purely algebraic means. In this paper, we prove two formulae that help to compute these operations. The first is a formula for exterior powers of external products. The second is a formula for exterior powers of n-cubes, i.e., of acyclic binary multi-complexes supported on [0,1]^n. These formulae provide evidence for the expectation that our exterior power operations agree with those defined by Hiller.

Text
Exterior Power Computations - Author's Original
Text
Exterior Power Computations - Accepted Manuscript

Accepted/In Press date: 11 February 2019
e-pub ahead of print date: 15 March 2019
Keywords: exterior power operations; higher K-groups; external products; Cauchy decomposition; cross-effect; modfied Milnor K-groups.

## Identifiers

Local EPrints ID: 427578
URI: http://eprints.soton.ac.uk/id/eprint/427578
ISSN: 0022-4049
PURE UUID: bfa60da7-e18f-4cc1-bb10-6266586db7f0
ORCID for Bernhard Koeck: orcid.org/0000-0001-6943-7874

## Catalogue record

Date deposited: 23 Jan 2019 17:30

## Contributors

Author: Thomas Harris
Author: Bernhard Koeck