Lefschetz numbers of iterates of the monodromy and truncated arcs
By Jan Denef, François Loeser. 2000
99 citations recorded by the source corpus.
Abstract We express the Lefschetz number of iterates of the monodromy of a function on a smooth complex algebraic variety in terms of the Euler characteristic of a space of truncated arcs. We also construct a canonical representative of the Milnor fibre in a suitable monodromic Grothendieck group.
Subfields: Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/2161c06f42e7e0675978108bf273e2bfd21face0
How researchers see this paper
The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.
In Geometry and Topology
In Mathematical Physics
Citations in the corpus
- Iterated vanishing cycles, convolution, and a motivic analogue of a conjecture of Steenbrink (2003, background): “Denef and Loeser showed in [5] and [8] (see also [9]) that Zg(T ) is a rational series by giving a formula for Zg(T ) in terms of a resolution of f .”
- Motivic invariants of arc-symmetric sets and blow-Nash equivalence (2003, methodology): “mula, which is a simplification of the one of [8], theorem 2.2.1 to our setting, uses the theory of motivic integration on arc spaces for real algebraic varieties (for motivic integration, we refer to [5, 6, 7, 8, 16, 21]). In particular we will use the change of variables formula, which is a fundame”
- Contact loci in arc spaces (2003, unknown): “imension P i νi(ki +1). In particular, for every irreducible component Wof Cont p(a) there is a unique multi-index νas above such that Contν(E) dominates W. A related result appears as Theorem 2.4 in [DL1]. Theorem A yields a quick proof of results of [Mus2] relating the dimensions of the arc spaces”
- Motivic Serre invariants, ramification, and the analytic Milnor fiber (2007, methodology): “7 with the computation in [24], Theorem 2.”