Nguyen Hong Duc (Thang Long University)

Title: Motivic Integration for Formal Schemes

Abstract: Motivated by the motivic integral identity conjecture by Kontsevich-Soibelman we develop systematically the theory of equivariant motivic integration for special formal schemes. We first introduce the notion of equivariant motivic integrals for special formal schemes extending Denef-Loeser's motivic integrals for varieties as well as Loeser-Sebag's motivic integrals for formal schemes topologically of finite type. We prove the change of variables formula for this new integral and the rationality of the corresponding Poincare series. As a consequence, we introduce the notion of motivic zeta function for formal series extending Denef-Loeser motivic zeta functions for regular functions.