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Variations on a question of Larsen and Lunts
Author(s):
Julien
Sebag
Journal:
Proc. Amer. Math. Soc.
138
(2010),
1231-1242.
MSC (2000):
Primary 14E05;
Secondary 14E07, 14R10
Posted:
December 1, 2009
MathSciNet review:
2578517
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Abstract:
Let  be a field of characteristic zero. Let  and  be two  -schemes of finite type having the same class in the Grothendieck ring of varieties. Is it true that  and  are piecewise isomorphic? This question, originally asked by Larsen and Lunts, and some of its consequences constitute the subject of this article.
References:
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- 1.
- Bittner, Franziska. The universal Euler characteristic for varieties of characteristic zero, Compos. Math. 140 (2004), no. 4, 1011-1032. MR 2059227 (2005d:14031)
- 2.
- Denef, Jan; Loeser, François. On some rational generating series occurring in arithmetic geometry. Geometric aspects of Dwork theory. Vols. I, II, 509-526, Walter de Gruyter, Berlin, 2004. MR 2099079 (2005h:11267)
- 3.
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- 4.
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 -space. Séminaire Bourbaki, Vol. 1994/95. Astérisque No. 237 (1996), Exp. No. 802, 5, 295-317. MR 1423629 (97m:14042) - 5.
- Larsen, Michael; Lunts, Valery A. Motivic measures and stable birational geometry. Mosc. Math. J. 3 (2003), no. 1, 85-95. MR 1996804 (2005a:14026)
- 6.
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- 7.
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- 8.
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Additional Information:
Julien
Sebag
Affiliation:
Institut de Mathématiques de Bordeaux, Université Bordeaux 1, 351 cours de la libération, 33405 Talence cedex, France
Address at time of publication:
Institut de Formation et de Recherche Mathématiques and Institut de Recherche Mathématiques de Rennes, 263 Avenue du Général Leclerc, CS 74205, 35042 Rennes cedex, France
Email:
julien.sebag@univ-rennes1.fr
DOI:
10.1090/S0002-9939-09-10179-X
PII:
S 0002-9939(09)10179-X
Received by editor(s):
March 2, 2009,
Received by editor(s) in revised form:
August 25, 2009
Posted:
December 1, 2009
Communicated by:
Ted Chinburg
Copyright of article:
Copyright
2009,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
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