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15 April 2006 Iterated vanishing cycles, convolution, and a motivic analogue of a conjecture of Steenbrink
Gil Guibert, François Loeser, Michel Merle
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Duke Math. J. 132(3): 409-457 (15 April 2006). DOI: 10.1215/S0012-7094-06-13232-5

Abstract

We prove a motivic analogue of Steenbrink's conjecture [25, Conjecture 2.2] on the Hodge spectrum (proved by M. Saito in [21]). To achieve this, we construct and compute motivic iterated vanishing cycles associated with two functions. We are also led to introduce a more general version of the convolution operator appearing in the motivic Thom-Sebastiani formula. Throughout the article we use the framework of relative equivariant Grothendieck rings of varieties endowed with an algebraic torus action

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Gil Guibert. François Loeser. Michel Merle. "Iterated vanishing cycles, convolution, and a motivic analogue of a conjecture of Steenbrink." Duke Math. J. 132 (3) 409 - 457, 15 April 2006. https://doi.org/10.1215/S0012-7094-06-13232-5

Information

Published: 15 April 2006
First available in Project Euclid: 1 April 2006

zbMATH: 1173.14301
MathSciNet: MR2219263
Digital Object Identifier: 10.1215/S0012-7094-06-13232-5

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Rights: Copyright © 2006 Duke University Press

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Vol.132 • No. 3 • 15 April 2006
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