Chai's Conjecture and Fubini properties of dimensional motivic   integration
  We prove that a conjecture of Chai on the additivity of the base change conductor for semi-abelian 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. 
R. Cluckers, F. Loeser, J. Nicaise
math.AG math.LO