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15 January 2020 Irrationality of motivic zeta functions
Michael J. Larsen, Valery A. Lunts
Duke Math. J. 169(1): 1-30 (15 January 2020). DOI: 10.1215/00127094-2019-0035

Abstract

Let K0(VarQ)[1/L] denote the Grothendieck ring of Q-varieties with the Lefschetz class inverted. We show that there exists a K3 surface X over Q such that the motivic zeta function ζX(t):=n[SymnX]tn regarded as an element in K0(VarQ)[1/L][[t]] is not a rational function in t, thus disproving a conjecture of Denef and Loeser.

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Michael J. Larsen. Valery A. Lunts. "Irrationality of motivic zeta functions." Duke Math. J. 169 (1) 1 - 30, 15 January 2020. https://doi.org/10.1215/00127094-2019-0035

Information

Received: 7 September 2018; Revised: 10 May 2019; Published: 15 January 2020
First available in Project Euclid: 21 November 2019

zbMATH: 07198454
MathSciNet: MR4047547
Digital Object Identifier: 10.1215/00127094-2019-0035

Subjects:
Primary: 14G10
Secondary: 11F80, 14F42, 14K15

Rights: Copyright © 2020 Duke University Press

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Vol.169 • No. 1 • 15 January 2020
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