Vol. 7, No. 4, 2013

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ISSN: 1944-7833 (e-only)
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Chai's conjecture and Fubini properties of dimensional motivic integration

Raf Cluckers, François Loeser and Johannes Nicaise

Vol. 7 (2013), No. 4, 893–915
Abstract

We prove that a conjecture of Chai on the additivity of the base change conductor for semiabelian varieties over a discretely valued field is equivalent to a Fubini property for the dimensions of certain motivic integrals. We prove this Fubini property when the valued field has characteristic zero.

Keywords
semiabelian varieties, motivic integration, base change conductor
Mathematical Subject Classification 2010
Primary: 14K15
Secondary: 03C65, 03C98, 11G10
Milestones
Received: 28 April 2011
Revised: 1 February 2013
Accepted: 3 March 2013
Published: 29 August 2013
Authors
Raf Cluckers
Laboratoire Painlevé
Université Lille 1
UMR CNRS 8524
Cité Scientifique
59655 Villeneuve d’Ascq
France
http://math.univ-lille1.fr/~cluckers
François Loeser
Institut de Mathématiques de Jussieu
Université Pierre et Marie Curie
UMR CNRS 7586
4 place Jussieu
75252 Paris
France
http://www.math.jussieu.fr/~loeser
Johannes Nicaise
Department of Mathematics
Katholieke Universiteit Leuven
Celestijnenlaan 200B
3001 Heverlee
Belgium
http://https://perswww.kuleuven.be/~u0025871/