logo_acta

Acta Mathematica Vietnamica

A Short Survey on the Integral Identity Conjecture and Theories of Motivic Integration

icon-email Lê Quy Thuong

Abstract

In Kontsevich-Soibelman’s theory of motivic Donaldson-Thomas invariants for 3-dimensional noncommutative Calabi-Yau varieties, the integral identity conjecture plays a crucial role as it involves the existence of these invariants. A purpose of this note is to show how the conjecture arises. Because of the integral identity’s nature, we shall give a quick tour on theories of motivic integration, which lead to a proof of the conjecture for algebraically closed ground fields of characteristic zero.