What is motivic measure?
Author:
Thomas C. Hales
Journal:
Bull. Amer. Math. Soc. 42 (2005), 119-135
MSC (2000):
Primary 14G20
DOI:
https://doi.org/10.1090/S0273-0979-05-01053-0
Published electronically:
January 28, 2005
MathSciNet review:
2133307
Full-text PDF
Abstract | References | Similar Articles | Additional Information
Abstract: This article gives an exposition of the theory of arithmetic motivic measure, as developed by J. Denef and F. Loeser.
- 1. R. Cluckers and F. Loeser, Fonctions constructibles et intégration motivique I, II, C. R. Math. Acad. Sci. Paris 339 (2004), no. 6, 411-416. MR 2092754
- 2. A. Craw, An introduction to motivic integration, 1999.
- 3. J. Denef and F. Loeser, Motivic Igusa functions, Journal of Algebraic Geometry 7, 505-537 (1998). MR 1618144 (99j:14021)
- 4. J. Denef and F. Loeser, Germs of arcs on singular algebraic varieties and motivic integration, Inventiones Mathematicae 135, 201-232 (1999). MR 1664700 (99k:14002)
- 5.
J. Denef and F. Loeser, Definable sets, motives and
-adic integrals, JAMS 14, No. 2, 429-469, 2000. MR 1815218 (2002k:14033)
- 6. J. Denef and F. Loeser, Motivic integration and the Grothendieck group of pseudo-finite fields, Proc. ICM, Vol. II (Beijing, 2002), 13-23, Higher Education Press, 2002. MR 1957016 (2004f:14040)
- 7. J. Denef and F. Loeser, On some rational generating series occurring in arithmetic geometry, to appear.
- 8. W. Fulton, Intersection Theory, second edition, Springer, 1998. MR 1644323 (99d:14003)
- 9. G. van der Geer and B. Moonen, Abelian Varieties, preliminary version of Chapter XI. The Fourier transform and the Chow ring, July 2003, http://turing.wins.uva.nl/bmoonen/boek/BookAV.html.
- 10. M. Kontsevich, lecture at Orsay, December 1995.
- 11. F. Loeser and J. Sebag, Motivic integration on smooth rigid varieties and invariants of degenerations, Duke Mathematical Journal 119, 315-344 (2003). MR 1997948 (2004g:14026)
- 12. E. Looijenga, Motivic measures. Séminaire Bourbaki, Vol. 1999/2000. Astérisque No. 276 (2002), 267-297. MR 1886763 (2003k:14010)
- 13. E. Lupercio and M. Poddar, The global McKay-Ruan correspondence via motivic integration, Bull. London Math. Soc. 36 (2004), no. 4, 509-515. MR 2069013
- 14.
J. Pas, Uniform
-adic cell decomposition and local zeta functions, J. reine angew. Math. 399 (1989), 137-172. MR 1004136 (91g:11142)
- 15. A. Scholl, Classical motives, in Motives (U. Jannsen, S. Kleiman, J-P. Serre, Eds.), Proc. Symp. Pure Math., Vol. 55, Part 1 (1994), 163-187, Amer. Math. Soc. MR 1265529 (95b:11060)
- 16. J. Sebag, Intégration motivique sur les schémas formels, Bull. Soc. Math. France 132 (2004), no. 1, 1-54. MR 2075915
Retrieve articles in Bulletin of the American Mathematical Society with MSC (2000): 14G20
Retrieve articles in all journals with MSC (2000): 14G20
Additional Information
Thomas C. Hales
Affiliation:
Department of Mathematics, University of Pittsburgh, Pittsburgh, Pennsylvania 15260
DOI:
https://doi.org/10.1090/S0273-0979-05-01053-0
Received by editor(s):
June 1, 2003
Published electronically:
January 28, 2005
Additional Notes:
Work supported by the NSF
This work is licensed under the Creative Commons Attribution License. To view a copy of this license, visit http://creativecommons.org/licenses/by/1.0/ or send a letter to Creative Commons, 559 Nathan Abbott Way, Stanford, California 94305, USA
Article copyright:
© Copyright 2005
Thomas C. Hales