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- Jan Denef, François Loeser
- 2001

This paper is a survey on arc spaces, a recent topic in algebraic geometry and singularity theory. The geometry of the arc space of an algebraic variety yields several new geometric invariants and… (More)

- Jan Denef, François Loeser
- 1999

Let k be a field of characteristic zero. We denote by M the Grothendieck ring of algebraic varieties over k (i.e. reduced separated schemes of finite type over k). It is the ring generated by symbols… (More)

- Jan Denef, François Loeser
- 1998

We define motivic analogues of Igusa's local zeta functions. These functions take their values in a Grothendieck group of Chow motives. They specialize to p-adic Igusa local zeta functions and to the… (More)

- Jan Denef, François Loeser
- 1992

Dans cet article nous definissons de nouveaux invariants pour les germes de fonctions analytiques complexes I et les polynomes complexes I, que nous appelons fonctions zeta topologiques Z f, top… (More)

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… (More)

- Jan Denef, François Loeser
- 2001

0.1. Let X be a scheme, reduced and separated, of finite type over Z. For p a prime number, one may consider the set X(Zp) of its Zp-rational points. For every n in N, there is a natural map πn :… (More)

- Jan Denef, François Loeser
- 1991

(1.1) Throughout this paper k always denotes a finite field Fq with q elements, and E a prime number not dividing q. The algebraic closure of a field K is denoted by / ( . Let ~b: k--+ C • be a… (More)

- Jan Denef, François Loeser
- 1999

We introduce motivic analogues of p-adic exponential integrals. We prove a basic multiplicativity property from which we deduce a motivic analogue of the Thom-Sebastiani Theorem. In particular, we… (More)

We prove that a (globally) subanalytic function $${f : X \subset {\bf Q}^{n}_{p} \rightarrow {\bf Q}_{p}}$$ which is locally Lipschitz continuous with some constant C is piecewise (globally on each… (More)

- François Loeser, J Sebag
- 2003

In the last years, motivic integration has shown to be a quite powerful tool in producing new invariants in birational geometry of algebraic varieties over a field k, say of characteristic zero, cf.… (More)