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ON THE COMMUTATIVITY OF PULL-BACK AND PUSH-FORWARD FUNCTORS ON MOTIVIC CONSTRUCTIBLE FUNCTIONS

Published online by Cambridge University Press:  14 May 2019

JORGE CELY  and
MICHEL RAIBAUT
JORGE CELY
Affiliation:
UNIVERSITÉ DE LILLE LABORATOIRE PAINLEVÉ CNRS - UMR 8524, CITÉ SCIENTIFIQUE 59655 VILLENEUVE D’ASCQ CEDEX, FRANCEE-mail: [email protected]
MICHEL RAIBAUT
Affiliation:
UNIVERSITY OF GRENOBLE ALPES UNIVERSITY OF SAVOIE MONT BLANC CNRS, LAMA, LE BOURGET-DU-LAC, 73376, FRANCEE-mail: [email protected]: raibautm.perso.math.cnrs.fr/site/michelraibaut.html
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Abstract

In this article, we study the commutativity between the pull-back and the push-forward functors on constructible functions in Cluckers–Loeser motivic integration.

Keywords

14E1803C9812L1226E30motivic integrationexponential constructible functionspull-back and pushforward functors
Type
Articles
Information
The Journal of Symbolic Logic , Volume 84 , Issue 3 , September 2019 , pp. 1252 - 1278
Copyright
Copyright © The Association for Symbolic Logic 2019 

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References

REFERENCES

Cluckers, R., Gordon, J., and Halupczok, I., Integrability of oscillatory functions on local fields: Transfer principles. Duke Mathematical Journal, vol. 163 (2014), no. 8, pp. 1549–1600.Google Scholar
Cluckers, R., Hales, T., and Loeser, F., Transfer principle for the fundamental lemma, On the Stabilization of the Trace Formula (Clozel, L., Harris, M., Labesse, J.-P., and Ngô, B.-C., editors), Stabilization of the Trace Formula, Shimura Varieties, and Arithmetic Applications, vol. 1, International Press, Somerville, MA, 2011, pp. 309–347.Google Scholar
Cluckers, R. and Loeser, F., Fonctions constructibles et intégration motivique. I. Comptes rendus de l’Académie des Sciences Paris, vol. 339 (2004), no. 6, pp. 411–416.Google Scholar
Cluckers, R. and Loeser, F., Fonctions constructibles et intégration motivique. II. Comptes rendus de l’Académie des Sciences Paris, vol. 339 (2004), no. 7, pp. 487–492.Google Scholar
Cluckers, R. and Loeser, F., Ax-Kochen-Eršov theorems for p-adic integrals and motivic integration, Geometric Methods in Algebra and Number Theory (Bogomolov, F. and Tschinkel, Y., editors), Progress in Mathematics, vol. 235, Birkhäuser Boston, Boston, MA, 2005, pp. 109–137.Google Scholar
Cluckers, R. and Loeser, F., Fonctions constructibles exponentielles, transformation de Fourier motivique et principe de transfert. Comptes rendus de l’Académie des Sciences Paris, vol. 341 (2005), no. 12, pp. 741–746.Google Scholar
Cluckers, R. and Loeser, F., Constructible motivic functions and motivic integration. Inventiones Mathematicae, vol. 173 (2008), no. 1, pp. 23–121.Google Scholar
Cluckers, R. and Loeser, F., Constructible exponential functions, motivic Fourier transform and transfer principle. Annals of Mathematics (2), vol. 171 (2010), no. 2, pp. 1011–1065.Google Scholar
Denef, J., The rationality of the Poincaré series associated to the p-adic points on a variety. Inventiones Mathematicae, vol. 77 (1984), no. 1, pp. 1–23.Google Scholar
Gordon, J. and Yaffe, Y., An overview of arithmetic motivic integration, Ottawa Lectures on Admissible Representations of Reductive p-adic Groups (Cunningham, C. and Nevins, M., editors), Fields Institute Monographs, vol. 26, American Mathematical Society, Providence, RI, 2009, pp. 113–149.Google Scholar
Heifetz, D. B., p-adic oscillatory integrals and wave front sets. Pacific Journal of Mathematics, vol. 116 (1985), no. 2, pp. 285–305.Google Scholar
Hörmander, L., The Analysis of Linear Partial Differential Operators I: Distribution Theory and Fourier Analysis, Grundlehren der mathematischen Wissenschaften, vol. 256, Springer-Verlag, Berlin, 1983.Google Scholar
Hrushovski, E. and Kazhdan, D., Integration in valued fields, Algebraic Geometry and Number Theory (Ginzburg, V., editor), Progress in Mathematics, vol. 253, Birkhäuser Boston, Boston, MA, 2006, pp. 261–405.Google Scholar
Igusa, J.-I., An Introduction to the Theory of Local Zeta Functions, AMS/IP Studies in Advanced Mathematics, vol. 14, American Mathematical Society, Providence, RI; International Press, Cambridge, MA, 2000.Google Scholar
Kontsevich, M., Lecture at Orsay (Décembre 7, 1995).Google Scholar
Pas, J., Uniform p-adic cell decomposition and local zeta functions. Journal für die Reine und Angewandte Mathematik, vol. 399 (1989), pp. 137–172.Google Scholar
Presburger, M. and Jabcquette, D., On the completeness of a certain system of arithmetic of whole numbers in which addition occurs as the only operation. History and Philosophy of Logic, vol. 12 (1991), no. 2, pp. 225–233.Google Scholar
Cluckers, R., Halupczok, I., Loeser, F., and Raibaut, M., Distributions and wave front sets in the uniform non-arhimedean setting. Transaction of the London Mathematical Society, vol. 5 (2018), no. 1, pp. 97–131.Google Scholar
Raibaut, M., Motivic wave front sets, arXiv:1810.10567.Google Scholar
van den Dries, L., Dimension of definable sets, algebraic boundedness and Henselian fields. Annals of Pure and Applied Logic, vol. 45 (1989), no. 2, pp. 189–209. Stability in model theory, II (Trento, 1987).Google Scholar