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
@article{1143935996,
author = {Guibert, Gil and Loeser, Fran\c cois and Merle, Michel},
title = {Iterated vanishing cycles, convolution, and a motivic analogue of a conjecture of Steenbrink},
journal = {Duke Math. J.},
volume = {131},
number = {1},
year = {2006},
pages = { 409-457},
language = {en},
url = {http://dml.mathdoc.fr/item/1143935996}
}
Guibert, Gil; Loeser, François; Merle, Michel. Iterated vanishing cycles, convolution, and a motivic analogue of a conjecture of Steenbrink. Duke Math. J., Tome 131 (2006) no. 1, pp. 409-457. http://gdmltest.u-ga.fr/item/1143935996/