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8 - Motivic integration in mixed characteristic with bounded ramification: a summary

Published online by Cambridge University Press:  07 October 2011

Raf Cluckers
Affiliation:
Université Lille
François Loeser
Affiliation:
École Normale Supérieure
Raf Cluckers
Affiliation:
Université de Lille
Johannes Nicaise
Affiliation:
Katholieke Universiteit Leuven, Belgium
Julien Sebag
Affiliation:
Université de Rennes I, France
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References

[1] N., Bourbaki, Topologie générale, Chapitres 5 à 10, Hermann 1974.Google Scholar
[2] C. L., Chai, Néron models for semiabelian varieties: congruence and change of base field, Asian J. Math. 4 (2000), 715–736.Google Scholar
[3] C. L., Chai, J. K., Yu, Congruences of Néron models for tori and the Artin conductor (with an appendix by E. de Shalit), Ann. Math. 154 (2001), 347–382.Google Scholar
[4] R., Cluckers, T., Hales, F., Loeser, Transfer Principle for the Fundamental Lemma, to appear in a book edited by M. Harris on “Stabilisation de la formule des traces, variétés de Shimura, et applications arithmétiques”, available at www.institut.math.jussieu.fr/projets/fa/bp0.html and arXiv:0712.0708.
[5] R., Cluckers, L., Lipshitz, Z., Robinson, Analytic cell decomposition and analytic motivic integration, Ann. Sci. École Norm. Sup., 39 (2006), 535–568.Google Scholar
[6] R., Cluckers, G., Comte, F., Loeser, Lipschitz continuity properties for p-adic semi-algebraic functions and subanalytic functions, Geom. Funct. Anal. 20 (2010), 68–87.Google Scholar
[7] R., Cluckers, L., Lipshitz, Fields with analytic structure, to appear in J. Eur. Math. Soc. (JEMS), 13 (2011), 1147–1223, arXiv:0908.2376.Google Scholar
[8] R., Cluckers, F., Loeser, b-minimality, Journal of Mathematical Logic, Vol. 7, No. 2, 195 - 227 (2007)Google Scholar
[9] R., Cluckers, F., Loeser, Constructible motivic functions and motivic integration, Invent. Math., Vol. 173, No. 1, 23–121 (2008).Google Scholar
[10] R., Cluckers, F., Loeser, Constructible exponential functions, motivic Fourier transform and transfer principle, Ann. Math. 171 (2010) 1011–1065.Google Scholar
[11] R., Cluckers, F., Loeser, Motivic integration in mixed characteristic with bounded ramification, preprint, arXiv:1102.3832.
[12] R., Cluckers, F., Loeser, J., Nicaise, Chai's conjecture and Fubini properties of dimensional motivic integration, preprint, arXiv:1102.5653.
[13] J., Denef, On the evaluation of certain p-adic integrals, Séminaire de théorie des nombres, Paris 1983–84, 25–47, Progr. Math., 59, Birkhäuser Boston, Boston, MA, 1985.Google Scholar
[14] J., Denef, F., Loeser, Germs of arcs on singular algebraic varieties and motivic integration, Invent. Math. 135 (1999), 201–232.Google Scholar
[15] J., Denef, F., Loeser, Motivic Igusa zeta functions, J. Algebraic Geom. 7 (1998), 505–537.Google Scholar
[16] J., Denef, F., Loeser, Definable sets, motives and p-adic integrals, J. Amer. Math. Soc., 14 (2001), 429–469.Google Scholar
[17] M., Kontsevich, Lecture at Orsay (December 7, 1995).
[18] E., Hrushovski, D., Kazhdan, Integration in valued fields, in Algebraic geometry and number theory, Progress in Mathematics 253, 261–405 (2006), Birkhäuser.Google Scholar
[19] F., Loeser, J., Sebag, Motivic integration on smooth rigid varieties and invariants of degenerations, Duke Math. J. 119 (2003), 315–344.Google Scholar
[20] D., Meuser, The meromorphic continuation of a zeta function of Weil and Igusa Type, Invent. math. 85 (1986), 493–514.Google Scholar
[21] J., Nicaise, A trace formula for rigid varieties, and motivic Weil generating series for formal schemesMath. Ann. 343 no. 2 (2009) 285–349.Google Scholar
[22] J., Pas, 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.Google Scholar
[23] J., Pas, Local zeta functions and Meuser's invariant functions, J. Number Theory 38 (1991), 287–299.Google Scholar
[24] J., Sebag, Intégration motivique sur les schémas formels, Bull. Soc. Math. France, 132 (2004), 1–54.Google Scholar
[25] Zhiwei, Yun, with appendix by J., Gordon, The fundamental lemma of Jacquet-Rallis, DukeMath. J. 156, no. 2 (2011), 167–227.Google Scholar

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