Motivic measures

Eduard Looijenga

Séminaire Bourbaki (1999-2000)

  • Volume: 42, page 267-297
  • ISSN: 0303-1179

How to cite


Looijenga, Eduard. "Motivic measures." Séminaire Bourbaki 42 (1999-2000): 267-297. <>.

author = {Looijenga, Eduard},
journal = {Séminaire Bourbaki},
keywords = {motivic zeta function; motivic convolution; families of varieties; Grothendieck ring; -jet spaces; motivic measures; stringy invariants of singularities; arc spaces; Thom-Sebastiani property; motivic McKay correspondence},
language = {eng},
pages = {267-297},
publisher = {Société Mathématique de France},
title = {Motivic measures},
url = {},
volume = {42},
year = {1999-2000},

AU - Looijenga, Eduard
TI - Motivic measures
JO - Séminaire Bourbaki
PY - 1999-2000
PB - Société Mathématique de France
VL - 42
SP - 267
EP - 297
LA - eng
KW - motivic zeta function; motivic convolution; families of varieties; Grothendieck ring; -jet spaces; motivic measures; stringy invariants of singularities; arc spaces; Thom-Sebastiani property; motivic McKay correspondence
UR -
ER -


  1. [1] D. Abramovich, K. Karu, K. Matsuki, J. Wlodarczyk, Torification and Factorization of Birational Maps, 30 p., Zbl1032.14003MR1896232
  2. [2] N. A'Campo, La fonction zêta d'une monodromie, Comment. Math. Helv.50 (1975), 233-248. Zbl0333.14008MR371889
  3. [3] G. Anderson, Cyclotomy and an extension of the Taniyama group, Comp. Math.57 (1986), 153-217. Zbl0591.14001MR827351
  4. [4] V. Batyrev, Birational Calabi-Yau n-folds have equal Betti numbers, in New trends in algebraic geometry, Klaus Hulek et al., eds., CUP, 1999, 1-11. Zbl0955.14028MR1714818
  5. [5] V. Batyrev, Stringy Hodge numbers of varieties with Gorenstein canonical singularities, in Integrable systems and algebraic geometry (Kobe/Kyoto, 1997). 1-32, World Sci. Publishing, River Edge, NJ, 1998. Zbl0963.14015MR1672108
  6. [6] V. Batyrev, Non-Archimedean integrals and stringy Euler numbers of logterminal pairs, J. Eur. Math. Soc.1 (1999), 5-33. Zbl0943.14004MR1677693
  7. [7] V. Batyrev AND D. Dais, Strong McKay correspondence, string-theoretic Hodge numbers and mirror symmetry, Topology35 (1996), 901-929. Zbl0864.14022MR1404917
  8. [8] A. Craw, An introduction to motivic integration, 23 pp., 9911179. MR2103724
  9. [9] P. Deligne, Intégration sur un cycle évanescent. Invent. Math.76 (1984), no. 1. 129-143. Zbl0538.13007MR739629
  10. [10] J. Denef, Local zeta functions and Euler characteristics. Duke Math. J.63 (1991), no. 3, 713-721. Zbl0738.11060MR1121152
  11. [11] J. Denef, Report on Igusa's local zeta function, in Séminaire Bourbaki, volume 1990/91, exposé 741. Astérisque201-202-203 (1991), 359-386. Zbl0749.11054MR1157848
  12. [12] J. Denef, F. Loeser, Caractéristiques d'Euler-Poincaré, fonctions zêta locales et modifications analytiques, J. Amer. Math. Soc.5 (1992), 705-720. Zbl0777.32017MR1151541
  13. [13] J. Denef, F. Loeser, Motivic Igusa zeta functions, J. Algebraic Geom., 7 (1998), 505-537. Zbl0943.14010MR1618144
  14. [14] J. Denef, F. Loeser, Germs of arcs on singular algebraic varieties and motivic integration, Invent. Math., 135 (1999), 201-232. Zbl0928.14004MR1664700
  15. [15] J. Denef, F. Loeser, Motivic exponential integrals and a motivic Thom-Sebastiani Theorem, Duke Math. J., 99 (1999), 285-309. Zbl0966.14015MR1708026
  16. [16] J. Denef, F. Loeser, Motivic integration, quotient singularities and the McKay correspondence, 20 p., Zbl1080.14001MR1905024
  17. [17] J. Denef, F. Loeser, Definable sets, motives and P-adic integrals, 45 p., Zbl1040.14010MR1815218
  18. [18] J. Denef, F. Loeser, Lefschetz numbers of the monodromy and truncated arcs, 10 p., 
  19. [19] J. Denef, F. Loeser, Geometry on arc spaces of algebraic varieties, 22 p., Zbl1079.14003MR1905328
  20. [20] M. Greenberg, Schemata over local rings, Ann. Math.73 (1961), 624-648. Zbl0115.39004MR126449
  21. [21] M. Greenberg, Rational points in discrete valuation rings, Publ. Math. LH.E.S.31 (1966), 59-64. Zbl0146.42201MR207700
  22. [22] M. Kapranov, The elliptic curve in the S-duality theory and Eisenstein series for Kac-Moody groups, 41 pp., 
  23. [23] M. Kontsevich, Lecture at Orsay (December 7, 1995). 
  24. [24] J. Nash JR., Arc structure of singularities, Duke Math. J., 81 (1995), 31-38. Zbl0880.14010MR1381967
  25. [25] J. Pas, Uniform p-adic cell decomposition and local zeta functions, J. f. d. reine u. angew. Math.399 (1989), 137-172. Zbl0666.12014MR1004136
  26. [26] M. Reid, La correspondance de McKay (en anglais), in Séminaire Bourbaki, exposé 867, Novembre 1999, 20 p., in this volume and at 9911195. Zbl0996.14006MR1886756
  27. [27] T. Shioda, T. Katsura, On Fermat varieties, Tohuku math. J.31 (1979), 97-115. Zbl0415.14022MR526513
  28. [28] J. Steenbrink, The spectrum of hypersurface singularities, in Théorie de Hodge, Luminy 1987, Astérisque179-180 (1989), 163-184. Zbl0725.14031MR1042806
  29. [29] A. Varchenko, Asymptotic Hodge structure in the vanishing cohomology, Math. USSR Izvestija18 (1982), 469-512. Zbl0489.14003
  30. [30] W. Veys, The topological zeta function associated to a function on a normal surface germ, Topology38 (1999), no. 2, 439-456. Zbl0947.32020MR1660317
  31. [31] W. Veys, Zeta functions and 'Kontsevich invariants' on singular varieties, 27 pp., AG/0003025. MR1848509

Citations in EuDML Documents

  1. Andrew R. Linshaw, Gerald W. Schwarz, Bailin Song, [unknown]
  2. Raphaël Rouquier, Catégories dérivées et géométrie birationnelle
  3. Michel Raibaut, Fibre de Milnor motivique à l’infini et composition avec un polynôme non dégénéré
  4. Julien Sebag, Intégration motivique sur les schémas formels
  5. Satoshi Koike, Adam Parusiński, Motivic-type invariants of blow-analytic equivalence
  6. E. Artal Bartolo, P. Cassou-Noguès, I. Luengo, A. Melle Hernández, Monodromy conjecture for some surface singularities
  7. Michel Raibaut, Singularités à l’infini et intégration motivique
  8. Michel Hickel, Sur quelques aspects de la géométrie de l'espace des arcs tracés sur un espace analytique

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