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- G. Alimonti, C. Arpesella, +88 authors Y. Zakharov
- 2001

Borexino, a real-time device for low energy neutrino spectroscopy is nearing completion of construction in the underground laboratories at Gran Sasso, Italy (LNGS). The experiment’s goal is the direct measurement of the flux of Be solar neutrinos of all flavors via neutrino-electron scattering in an ultra-pure scintillation liquid. Seeded by a series of… (More)

- François Loeser
- 1999

Let X be an algebraic variety, not necessarily smooth, over a field k of characteristic zero. We denote by L(X) the k-scheme of formal arcs on X : K-points of L(X) correspond to formal arcs SpecK[[t]] → X , for K any field containing k. In a recent paper [8], we developped an integration theory on the space L(X) with values in M̂, a certain ring completion… (More)

- F. Loeser
- 1995

where the product is over all reflection hyperplanes of G. Let A : V/G -+ @ be the map induced by 6, thus A is the discriminant of G. A subgroup of G is called parabolic if it is generated by all reflections of G fixing elementwise a given subspace of V. The degrees of G are denoted by dl , d2, . . . , d,,. We call a degree of G primitive if it is bigger… (More)

Motivic integration is a powerful technique to prove that certain quantities associated to algebraic varieties are birational invariants or are independent of a chosen resolution of singularities. We survey our recent work on an extension of the theory of motivic integration, called arithmetic motivic integration. We developed this theory to understand how… (More)

We develop a theory of motivic integration for smooth rigid varieties. As an application we obtain a motivic analogue for rigid varieties of Serre’s invariant for p-adic varieties. Our construction provides new geometric birational invariants of degenerations of algebraic varieties. For degenerations of Calabi-Yau varieties, our results take a stronger form.

- François Loeser
- 2008

We introduce spaces of exponential constructible functions in the motivic setting for which we construct direct image functors in the absolute and relative settings. This allows us to define a motivic Fourier transformation for which we get various inversion statements. We also define spaces of motivic Schwartz-Bruhat functions on which motivic Fourier… (More)

- François Loeser
- 2004

This paper is concerned with extending classical results à la Ax-Kochen-Eršov to p-adic integrals in a motivic framework. The first section is expository, starting from Artin’s conjecture and the classical work of Ax, Kochen, and Eršov and ending with recent work of Denef and Loeser giving a motivic version of the results of Ax, Kochen, and Eršov. In that… (More)

1.1. In this paper, intended to be the first in a series, we lay new general foundations for motivic integration and give answers to some important issues in the subject. Since its creation by Maxim Kontsevich [23], motivic integration developed quickly and has spread out in many directions. In a nutshell, in motivic integration, numbers are replaced by… (More)

- Riccardo Benedetti, François Loeser, Jean-Jacques Risler
- Discrete & Computational Geometry
- 1991

- Jennifer Beineke, Jason Rosenhouse, +6 authors Takeshi Tsuji
- 2010

Let V be a quasi-projective algebraic variety over a nonarchimedean valued field. We introduce topological methods into the model theory of valued fields, define an analogue V̂ of the Berkovich analytification V an of V , and deduce several new results on Berkovich spaces from it. In particular we show that V an retracts to a finite simplicial complex and… (More)