Chai's Conjecture and Fubini properties of dimensional motivic integration

TL;DR

This paper links Chai's conjecture on base change conductors of semi-abelian varieties to a Fubini property in motivic integration, proving the property in characteristic zero fields, thus advancing understanding in algebraic geometry.

Contribution

It establishes the equivalence between Chai's conjecture and a Fubini property for motivic integrals, and proves this property in characteristic zero fields.

Findings

Chai's conjecture is equivalent to a Fubini property for motivic integrals.

The Fubini property is proven for fields with characteristic zero.

The work connects algebraic geometry conjectures with motivic integration properties.

Abstract

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.