Iterated vanishing cycles, convolution, and a motivic analogue of a conjecture of Steenbrink
By G. Guibert, François Loeser, M. Merle. 2003
93 citations recorded by the source corpus.
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.
Subfields: Algebra and Number Theory, Discrete Mathematics and Combinatorics, Geometry and Topology
View Paper: https://www.semanticscholar.org/paper/33573192962f10e41bd7819c0e81c5c038033c9e
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In Algebra and Number Theory
In Discrete Mathematics and Combinatorics
In Geometry and Topology
Citations in the corpus
- A trace formula for rigid varieties, and motivic Weil generating series for formal schemes (2007, background): “ way, since the normalization Rsof Rin Ksis not a discrete valuation ring. We will define a motivic object by taking a limit of motivic integrals over finite ramifications of X, instead. Definition 7.35 ([24], (2.8)). There is a unique M X0-linear morphism lim T→∞ : M X0 LaTb 1−LaTb (a,b)∈Z×N∗ −→ M X0”