Séries de Poincaré motiviques d'un germe d'hypersurface irréductible quasi-ordinaire
Équations différentielles et singularités. En l'honneur de J. M. Aroca, Astérisque, no. 323 (2009), pp. 371-396. 
@incollection{AST_2009__323__371_0,
     author = {Rond, Guillaume},
     title = {S\'eries de {Poincar\'e} motiviques d'un germe d'hypersurface irr\'eductible quasi-ordinaire},
     booktitle = {\'Equations diff\'erentielles et singularit\'es. En l'honneur de J. M. Aroca},
     editor = {Cano F. and Loray F. and Moralez-Ruiz J. J. and Sad P. and Spivakovsky M.},
     series = {Ast\'erisque},
     pages = {371--396},
     publisher = {Soci\'et\'e math\'ematique de France},
     number = {323},
     year = {2009},
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     url = {http://www.numdam.org/item/AST_2009__323__371_0/}
}
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Rond, Guillaume. Séries de Poincaré motiviques d'un germe d'hypersurface irréductible quasi-ordinaire, dans Équations différentielles et singularités. En l'honneur de J. M. Aroca, Astérisque, no. 323 (2009), pp. 371-396. http://www.numdam.org/item/AST_2009__323__371_0/

[1] S. Abhyankar - On the ramification of algebraic functions, Amer. J. Math. 77 (1955), p. 575-592. | DOI | MR | Zbl

[2] E. Artal Bartolo, P. Cassou-Noguès, I. Luengo & A. Melle Hernandez - Quasi-ordinary power series and their zeta functions, Mem. Amer. Math. Soc. 178 (2005). | MR | Zbl

[3] H. Cobo Pablos & P. D. González-Pérez - en préparation.

[4] J. Denef - The rationality of the Poincaré series associated to the p-adic points on a variety, Invent Math. 77 (1984), p. 1-23. | DOI | EuDML | MR | Zbl

[5] J. Denef & F. Loeser - Motivic Igusa zeta functions, J. Algebraic Geom. 7 (1998), p. 505-537. | MR | Zbl

[6] J. Denef & F. Loeser, Germs of arcs on singular algebraic varieties and motivic integration, Invent. Math. 135 (1999), p. 201-232. | DOI | MR | Zbl

[7] J. Denef & F. Loeser, Definable sets, motives and p-adic integrals, J. Amer. Math. Soc. 14 (2001), p. 429-469. | DOI | MR | Zbl

[8] J. Denef & F. Loeser, Geometry on arc spaces of algebraic varieties, in European Congress of Mathematics, Vol. I (Barcelona, 2000), Progr. Math., vol. 201, Birkhäuser, 2001, p. 327-348. | MR | Zbl

[9] W. Fulton - Introduction to toric varieties, Annals of Mathematics Studies, vol. 131, Princeton University Press, 1993, The William H. Roever Lectures in Geometry. | MR | Zbl

[10] Y.-N. Gau - Embedded topological classification of quasi-ordinary singularities, Mem. Amer. Math. Soc. 74 (1988), p. 109-129. | MR | Zbl

[11] P. D. González-Pérez - The semigroup of a quasi-ordinary hypersurface, J. Inst. Math. Jussieu 2 (2003), p. 383-399. | DOI | MR | Zbl

[12] P. D. González-Pérez, Toric embedded resolutions of quasi-ordinary hypersurface singularities, Ann. Inst. Fourier (Grenoble) 53 (2003), p. 1819-1881. | DOI | EuDML | Numdam | MR | Zbl

[13] M. J. Greenberg - Rational points in Henselian discrete valuation rings, Publ. Math. I.H.É.S. 31 (1966), p. 59-64. | DOI | EuDML | Numdam | MR

[14] T. C. Hales - What is motivic measure?, Bull Amer. Math. Soc. (N.S.) 42 (2005), p. 119-135. | DOI | MR | Zbl

[15] M. Kontsevich - Cours à Orsay, 7 décembre 1995.

[16] M. Lejeune-Jalabert - La série de Denef-Loeser d'une branche plane, notes informelles, 2001.

[17] M. Lejeune-Jalabert & A. J. Reguera - The Denef-Loeser series for toric surface singularities, in Proceedings of the International Conference on Algebraic Geometry and Singularities (Spanish) (Sevilla, 2001), vol. 19, 2003, p. 581-612. | EuDML | MR | Zbl

[18] M. Lejeune-Jalabert & A. J. Reguera-López - Arcs and wedges on sandwiched surface singularities, Amer. J. Math. 121 (1999), p. 1191-1213. | DOI | MR | Zbl

[19] J. Lipman - Quasi-ordinairy singularities of embedded surfaces, Thèse, Université de Harvard, 1965. | MR

[20] J. Lipman, Topological invariants of quasi-ordinary singularities, Mem. Amer. Math. Soc. 74 (1988), p. 1-107. | MR | Zbl

[21] J. Nicaise - Arcs and resolution of singularities, Manuscripta Math. 116 (2005), p. 297-322. | DOI | MR | Zbl

[22] J. Nicaise, Motivic generating series for toric surface singularities, Math. Proc. Cambridge Philos. Soc. 138 (2005), p. 383-400. | DOI | MR | Zbl

[23] J. Pas - Uniform p-adic cell decomposition and local zeta functions, J. reine angew. Math. 399 (1989), p. 137-172. | EuDML | MR | Zbl

[24] O. Zariski - Le problème des modules pour les branches planes, École Polytechnique, 1973, Cours donné au Centre de Mathématiques de l'École Polytechnique, Paris. | MR | Zbl