Equivariant motivic integration and proof of the integral identity conjecture for regular functions

TL;DR

This paper extends motivic integration to an equivariant setting and uses it to prove the integral identity conjecture for regular functions, advancing the understanding of motivic measures and their applications.

Contribution

It introduces an equivariant version of motivic integration and proves the integral identity conjecture for regular functions, a significant theoretical advancement.

Findings

Proved the full integral identity conjecture for regular functions.

Developed the equivariant motivic integration framework.

Enhanced the theoretical foundation of motivic integration.

Abstract

We develop the Denef-Loeser motivic integration to the equivariant motivic integration and use it to prove the full integral identity conjecture for regular functions.