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What is motivic measure?
Author(s):
Thomas
C.
Hales
Journal:
Bull. Amer. Math. Soc.
42
(2005),
119-135.
MSC (2000):
Primary 14G20
Posted:
January 28, 2005
MathSciNet review:
2133307
Retrieve article in:
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References |
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Additional information
Abstract:
This article gives an exposition of the theory of arithmetic motivic measure, as developed by J. Denef and F. Loeser.
References:
-
- 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
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Additional Information:
Thomas
C.
Hales
Affiliation:
Department of Mathematics, University of Pittsburgh, Pittsburgh, Pennsylvania 15260
DOI:
10.1090/S0273-0979-05-01053-0
PII:
S 0273-0979(05)01053-0
Received by editor(s):
June 1, 2003
Posted:
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
Copyright of article:
Copyright
2005,
Thomas C. Hales
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