A proof of the integral identity conjecture, II

TL;DR

This paper proves the integral identity conjecture using motivic integration within a localized Grothendieck ring framework over any characteristic zero base field.

Contribution

It provides a proof of the integral identity conjecture employing Cluckers-Loeser's motivic integration theory in a generalized setting.

Findings

Proves the integral identity conjecture in a broad algebraic context.

Utilizes motivic integration to establish the conjecture.

Extends the conjecture's proof to arbitrary base fields of characteristic zero.

Abstract

In this note, using Cluckers-Loeser's theory of motivic integration, we prove the integral identity conjecture with framework a localized Grothendieck ring of varieties over an arbitrary base field of characteristic zero.