Variations on a question of Larsen and Lunts
HTML articles powered by AMS MathViewer
- by Julien Sebag PDF
- Proc. Amer. Math. Soc. 138 (2010), 1231-1242 Request permission
Abstract:
Let $k$ be a field of characteristic zero. Let $X$ and $X’$ be two $k$-schemes of finite type having the same class in the Grothendieck ring of varieties. Is it true that $X$ and $X’$ are piecewise isomorphic? This question, originally asked by Larsen and Lunts, and some of its consequences constitute the subject of this article.References
- Franziska Bittner, The universal Euler characteristic for varieties of characteristic zero, Compos. Math. 140 (2004), no. 4, 1011–1032. MR 2059227, DOI 10.1112/S0010437X03000617
- Jan Denef and François Loeser, On some rational generating series occurring in arithmetic geometry, Geometric aspects of Dwork theory. Vol. I, II, Walter de Gruyter, Berlin, 2004, pp. 509–526. MR 2099079
- Amit Hogadi, Products of Brauer-Severi surfaces, Proc. Amer. Math. Soc. 137 (2009), no. 1, 45–50. MR 2439423, DOI 10.1090/S0002-9939-08-09450-1
- Hanspeter Kraft, Challenging problems on affine $n$-space, Astérisque 237 (1996), Exp. No. 802, 5, 295–317. Séminaire Bourbaki, Vol. 1994/95. MR 1423629
- Michael Larsen and Valery A. Lunts, Motivic measures and stable birational geometry, Mosc. Math. J. 3 (2003), no. 1, 85–95, 259 (English, with English and Russian summaries). MR 1996804, DOI 10.17323/1609-4514-2003-3-1-85-95
- Qing Liu, Algebraic geometry and arithmetic curves, Oxford Graduate Texts in Mathematics, vol. 6, Oxford University Press, Oxford, 2002. Translated from the French by Reinie Erné; Oxford Science Publications. MR 1917232
- Liu, Qing; Sebag, Julien. The Grothendieck ring of varieties and piecewise isomorphisms, to appear in Math. Z.
- Julien Sebag, Intégration motivique sur les schémas formels, Bull. Soc. Math. France 132 (2004), no. 1, 1–54 (French, with English and French summaries). MR 2075915, DOI 10.24033/bsmf.2458
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
- Received by editor(s): March 2, 2009
- Received by editor(s) in revised form: August 25, 2009
- Published electronically: December 1, 2009
- Communicated by: Ted Chinburg
- © Copyright 2009
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 138 (2010), 1231-1242
- MSC (2000): Primary 14E05; Secondary 14E07, 14R10
- DOI: https://doi.org/10.1090/S0002-9939-09-10179-X
- MathSciNet review: 2578517