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15 August 2017 The annihilator of the Lefschetz motive
Inna Zakharevich
Duke Math. J. 166(11): 1989-2022 (15 August 2017). DOI: 10.1215/00127094-0000016X

Abstract

In this article, we study a spectrum K(Vk) such that π0K(Vk) is the Grothendieck ring of varieties and such that the higher homotopy groups contain more geometric information about the geometry of varieties. We use the topology of this spectrum to analyze the structure of K0[Vk] and to show that classes in the kernel of multiplication by [A1] can always be represented as [X][Y], where [X][Y], X×A1, and Y×A1 are not piecewise-isomorphic, but [X×A1]=[Y×A1] in K0[Vk]. Along the way, we present a new proof of the result of Larsen–Lunts on the structure on K0[Vk]/([A1]).

Citation

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Inna Zakharevich. "The annihilator of the Lefschetz motive." Duke Math. J. 166 (11) 1989 - 2022, 15 August 2017. https://doi.org/10.1215/00127094-0000016X

Information

Received: 29 September 2015; Revised: 20 November 2016; Published: 15 August 2017
First available in Project Euclid: 28 April 2017

zbMATH: 06775425
MathSciNet: MR3694563
Digital Object Identifier: 10.1215/00127094-0000016X

Subjects:
Primary: 19E99
Secondary: 14E99

Keywords: algebraic K-theory , birational geometry , Grothendieck ring of varieties

Rights: Copyright © 2017 Duke University Press

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Vol.166 • No. 11 • 15 August 2017
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