Algebra & Number Theory

Chai's conjecture and Fubini properties of dimensional motivic integration

Raf Cluckers, François Loeser, and Johannes Nicaise

Full-text: Open access

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.

Article information

Source
Algebra Number Theory, Volume 7, Number 4 (2013), 893-915.

Dates
Received: 28 April 2011
Revised: 1 February 2013
Accepted: 3 March 2013
First available in Project Euclid: 20 December 2017

Permanent link to this document
https://projecteuclid.org/euclid.ant/1513729985

Digital Object Identifier
doi:10.2140/ant.2013.7.893

Mathematical Reviews number (MathSciNet)
MR3095230

Zentralblatt MATH identifier
1312.14104

Subjects
Primary: 14K15: Arithmetic ground fields [See also 11Dxx, 11Fxx, 11G10, 14Gxx]
Secondary: 03C65: Models of other mathematical theories 03C98: Applications of model theory [See also 03C60] 11G10: Abelian varieties of dimension > 1 [See also 14Kxx]

Keywords
semiabelian varieties motivic integration base change conductor

Citation

Cluckers, Raf; Loeser, François; Nicaise, Johannes. Chai's conjecture and Fubini properties of dimensional motivic integration. Algebra Number Theory 7 (2013), no. 4, 893--915. doi:10.2140/ant.2013.7.893. https://projecteuclid.org/euclid.ant/1513729985


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