A PROOF OF THE l-ADIC VERSION OF THE INTEGRAL IDENTITY CONJECTURE FOR POLYNOMIALS

It is well known that the integral identity conjecture is of prime importance in Kontsevich-Soibelman's theory of motivic Donaldson-Thomas invariants for non-commutative Calabi-Yau threefolds. In this article we consider its numerical version and give a complete demonstration of the case where the potential is a polynomial and the ground field is algebraically closed. The fundamental tool is the Berkovich spaces whose crucial point is how to use the comparison theorem for nearby cycles as well as the Kunneth isomorphism for cohomology with compact support.