@article{ASENS_2006_4_39_4_535_0,
author = {Cluckers, Raf and Lipshitz, Leonard and Robinson, Zachary},
title = {Analytic cell decomposition and analytic motivic integration},
journal = {Annales scientifiques de l'\'Ecole Normale Sup\'erieure},
pages = {535--568},
year = {2006},
publisher = {Elsevier},
volume = {Ser. 4, 39},
number = {4},
doi = {10.1016/j.ansens.2006.03.001},
mrnumber = {2290137},
zbl = {05125019},
language = {en},
url = {https://www.numdam.org/articles/10.1016/j.ansens.2006.03.001/}
}
TY - JOUR AU - Cluckers, Raf AU - Lipshitz, Leonard AU - Robinson, Zachary TI - Analytic cell decomposition and analytic motivic integration JO - Annales scientifiques de l'École Normale Supérieure PY - 2006 SP - 535 EP - 568 VL - 39 IS - 4 PB - Elsevier UR - https://www.numdam.org/articles/10.1016/j.ansens.2006.03.001/ DO - 10.1016/j.ansens.2006.03.001 LA - en ID - ASENS_2006_4_39_4_535_0 ER -
%0 Journal Article %A Cluckers, Raf %A Lipshitz, Leonard %A Robinson, Zachary %T Analytic cell decomposition and analytic motivic integration %J Annales scientifiques de l'École Normale Supérieure %D 2006 %P 535-568 %V 39 %N 4 %I Elsevier %U https://www.numdam.org/articles/10.1016/j.ansens.2006.03.001/ %R 10.1016/j.ansens.2006.03.001 %G en %F ASENS_2006_4_39_4_535_0
Cluckers, Raf; Lipshitz, Leonard; Robinson, Zachary. Analytic cell decomposition and analytic motivic integration. Annales scientifiques de l'École Normale Supérieure, Série 4, Tome 39 (2006) no. 4, pp. 535-568. doi: 10.1016/j.ansens.2006.03.001
[1] , , Diophantine problems over local fields I, II, Amer. J. Math. 87 (1965) 605-648, Diophantine problems over local fields III, Ann. of Math. 83 (1966) 437-456. | Zbl | MR
[2] , , , Non-Archimedean Analysis, Springer, Berlin, 1984. | Zbl | MR
[3] , Dimension theory and parameterized normalization for D-semianalytic sets over non-Archimedean fields, J. Symbolic Logic 70 (2005) 593-618. | MR | Zbl
[4] , Analytic p-adic cell decomposition and integrals, Trans. Amer. Math. Soc. 356 (2004) 1489-1499, math.NT/0206161. | Zbl | MR
[5] Cluckers R., Lipshitz L., Fields with analytic structure, Preprint. | MR | Zbl
[6] , , Constructible motivic functions and motivic integration, math.AG/0410203. | Zbl
[7] , , Fonctions constructibles et intégration motivique I, Comptes rendus de l'Académie des Sciences 339 (2004) 411-416, math.AG/0403349. | Zbl | MR
[8] , , Fonctions constructibles et intégration motivique II, Comptes rendus de l'Académie des Sciences 339 (2004) 487-492, math.AG/0403350. | Zbl | MR
[9] , , Ax-Kochen-Eršov theorems for p-adic integrals and motivic integration, in: Geometric Methods in Algebra and Number Theory, Progr. Math., vol. 235, Birkhäuser Boston, 2005, pp. 109-137. | MR | Zbl
[10] , , Fonctions constructibles exponentielles, transformation de Fourier motivique et principe de transfert, Comptes rendus de l'Académie des Sciences 341 (2005) 741-746, math.NT/0509723. | Zbl | MR
[11] , Decision procedures for real and p-adic fields, Comm. Pure Appl. Math. 22 (1969) 131-151. | Zbl | MR
[12] , The rationality of the Poincaré series associated to the p-adic points on a variety, Inventiones Mathematicae 77 (1984) 1-23. | Zbl | MR | EuDML
[13] , On the evaluation of certain p-adic integrals, in: Séminaire de théorie des nombres, Paris 1983-84, Progr. Math., vol. 59, Birkhäuser Boston, 1985, pp. 25-47. | Zbl | MR
[14] , p-adic semialgebraic sets and cell decomposition, Journal für die reine und angewandte Mathematik 369 (1986) 154-166. | Zbl | MR | EuDML
[15] , , Germs of arcs on singular algebraic varieties and motivic integration, Inventiones Mathematicae 135 (1999) 201-232. | Zbl | MR
[16] , , Definable sets, motives and p-adic integrals, J. Amer. Math. Soc. 14 (2) (2001) 429-469. | Zbl | MR
[17] , , On some rational generating series occurring in arithmetic geometry, in: , , , , (Eds.), Geometric Aspects of Dwork Theory 1, de Gruyter, Berlin, 2004, pp. 509-526, math.NT/0212202. | Zbl | MR
[18] , , p-adic and real subanalytic sets, Ann. of Math. 128 (1988) 79-138. | Zbl | MR
[19] , Analytic Ax-Kochen-Ershov theorems, in: Contemporary Mathematics, vol. 131, 1992, pp. 379-398. | Zbl | MR
[20] van den Dries L., notes on cell decomposition.
[21] , , , One-dimensional p-adic subanalytic sets, J. London Math. Soc. (2) 59 (1999) 1-20. | Zbl | MR
[22] , Valuation Theory, Springer, Berlin, 1972. | Zbl | MR
[23] , , Géométrie analytique rigide et applications, Progr. Math., vol. 18, Birkhäuser, Basel, 1981. | Zbl | MR
[24] , , Rigid Geometry and Applications, Progr. Math., vol. 218, Birkhäuser, Basel, 2004. | Zbl
[25] , An algebraic integration, in: Mathematics: Frontiers and Perspectives, AMS, Providence, RI, 2000, pp. 93-115. | Zbl | MR
[26] , Quantifier elimination for Henselian fields relative to additive and multiplicative congruences, Israel J. Math. 85 (1994) 277-306. | Zbl | MR
[27] Lang S., Algebra, Addison-Wesley, 1965. | Zbl | MR
[28] , , Intégration des fonctions sous-analytiques et volumes des sous-ensembles sous-analytiques, Ann. Inst. Fourier 48 (3) (1998) 755-767, (in French). | Zbl | MR | Numdam
[29] , Rigid subanalytic sets, Amer. J. Math. 115 (1993) 77-108. | Zbl | MR
[30] , , Rigid subanalytic subsets of the line and the plane, Amer. J. Math. 118 (1996) 493-527. | Zbl | MR
[31] , , Rigid subanalytic subsets of curves and surfaces, J. London Math. Soc. (2) 59 (1999) 895-921. | Zbl | MR
[32] , , Rings of separated power series, Astérisque 264 (2000) 3-108. | MR | Numdam
[33] , , Model completeness and subanalytic sets, Astérisque 264 (2000) 109-126.
[34] , , Uniform properties of rigid subanalytic sets, Trans. Amer. Math. Soc. 357 (1) (2005) 4349-4377. | Zbl | MR
[35] , , Motivic integration on smooth rigid varieties and invariants of degenerations, Duke Math. J. 119 (2) (2003) 315-344. | Zbl | MR
[36] , Rationality of p-adic Poincaré series: uniformity in p, Ann. Pure Appl. Logic 49 (1) (1990) 31-74. | Zbl | MR
[37] , , Invariant de Serre et fibre de Milnor analytique, Available at:, http://www.wis.kuleuven.ac.be/algebra/artikels/artikelse.htm, (in French).
[38] , Uniform p-adic cell decomposition and local zeta-functions, Journal für die reine und angewandte Mathematik 399 (1989) 137-172. | Zbl | MR | EuDML
[39] , Cell decomposition and local zeta-functions in a tower of unramified extensions of a p-adic field, Proc. London Math. Soc. 60 (1990) 37-67. | Zbl | MR
[40] , Quantifier elimination for the relative Frobenius, in: , , (Eds.), Valuation Theory and Its Applications, vol. II, Conference Proceedings of the International Conference on Valuation Theory (Saskatoon, 1999), Fields Institute Communications Series, AMS, Providence, RI, 2003, pp. 323-352. | Zbl | MR
[41] , Rationalité des séries de Poincaré et des fonctions zêta motiviques, Manuscripta Math. 115 (2) (2004) 125-162, (in French). | Zbl | MR
[42] , Intégration motivique sur les schémas formels, Bull. Soc. Math. France 132 (1) (2004) 1-54, (in French). | Zbl | MR | Numdam | EuDML
Cité par Sources :






