On introduit un formalisme d'images directes pour les fonctions constructibles motiviques. On en tire une version très générale de l'intégration motivique pour laquelle un théorème de changement de variables est établi. Ces constructions admettent une généralisation au cadre relatif, ce qui permet également de développer une version relative de l'intégration motivique.
We introduce a direct image formalism for constructible motivic functions. One deduces a very general version of motivic integration for which a change of variables theorem is proved. These constructions are generalized to the relative framework, in which we develop a relative version of motivic integration.
Accepté le :
Publié le :
Raf Cluckers 1 ; François Loeser 2
@article{CRMATH_2004__339_6_411_0, author = {Raf Cluckers and Fran\c{c}ois Loeser}, title = {Fonctions constructibles et int\'egration motivique {I}}, journal = {Comptes Rendus. Math\'ematique}, pages = {411--416}, publisher = {Elsevier}, volume = {339}, number = {6}, year = {2004}, doi = {10.1016/j.crma.2004.06.026}, language = {fr}, }
Raf Cluckers; François Loeser. Fonctions constructibles et intégration motivique I. Comptes Rendus. Mathématique, Volume 339 (2004) no. 6, pp. 411-416. doi : 10.1016/j.crma.2004.06.026. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2004.06.026/
[1] Fonctions constructibles et intégration motivique II, C. R. Acad. Sci. Paris, Ser. I, Volume 339 (2004)
[2] R. Cluckers, F. Loeser, Constructible motivic functions and motivic integration, en préparation
[3] Germs of arcs on singular algebraic varieties and motivic integration, Invent. Math., Volume 135 (1999), pp. 201-232
[4] Definable sets, motives and p-adic integrals, J. Amer. Math. Soc., Volume 14 (2001), pp. 429-469
[5] Dimension of definable sets, algebraic boundedness and Henselian fields, Ann. Pure Appl. Logic, Volume 45 (1989), pp. 189-209
[6] M. Kontsevich, Exposé à Orsay, 7 décembre 1995
[7] Uniform p-adic cell decomposition and local zeta functions, J. Reine Angew. Math., Volume 399 (1989), pp. 137-172
- Evaluation of motivic functions, non-nullity, and integrability in fibers, Advances in Mathematics, Volume 409 (2022), p. 108635 | DOI:10.1016/j.aim.2022.108635
- Motivic Wave Front Sets, International Mathematics Research Notices, Volume 2021 (2021) no. 17, p. 13075 | DOI:10.1093/imrn/rnz196
- A Complexity Theory of Constructible Functions and Sheaves, Foundations of Computational Mathematics, Volume 15 (2015) no. 1, p. 199 | DOI:10.1007/s10208-014-9222-z
- Constructible exponential functions, motivic Fourier transform and transfer principle, Annals of Mathematics, Volume 171 (2010) no. 2, p. 1011 | DOI:10.4007/annals.2010.171.1011
- Constructible motivic functions and motivic integration, Inventiones mathematicae, Volume 173 (2008) no. 1, p. 23 | DOI:10.1007/s00222-008-0114-1
- Integration of positive constructible functions against Euler characteristic and dimension, Journal of Pure and Applied Algebra, Volume 208 (2007) no. 2, p. 691 | DOI:10.1016/j.jpaa.2006.03.005
Cité par 6 documents. Sources : Crossref
Commentaires - Politique