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Exterior power operations
on higher $K$-groups via binary complexes
Tom Harris, Bernhard Köck and Lenny Taelman |
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Vol. 2 (2017), No. 3, 409–450
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Abstract |
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We use Grayson’s binary multicomplex presentation of algebraic -theory to give a new construction of exterior power operations on the higher -groups of a (quasicompact) scheme. We show that these operations satisfy the axioms of a -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 -ring on one generator. |
Keywords
exterior power operations, binary complexes, higher
algebraic $K$-theory, lambda ring, Dold–Kan correspondence,
Dold–Puppe construction, simplicial tensor product,
plethysm problem, polynomial functor, Schur algebra
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Mathematical Subject Classification 2010
Primary: 19D99
Secondary: 13D15, 14F99, 19E08, 20G05
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Milestones
Received: 20 July 2016
Revised: 5 September 2016
Accepted: 16 October 2016
Published: 1 June 2017
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Authors |
| Tom Harris | |
| University Printing House Shaftesbury Avenue Cambridge CB2 8BS United Kingdom |
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| Bernhard Köck | |
| Mathematical Sciences University of Southampton Highfield Southampton SO17 1BJ United Kingdom |
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| Lenny Taelman | |
| Korteweg-de Vries Instituut Universiteit van Amsterdam P.O. Box 94248 1090 GE Amsterdam Netherlands |
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