Motivic integration on formal schemes. (Intégration motivique sur les schémas formels.) (French) Zbl 1084.14012

Sebag, Julien

Bull. Soc. Math. Fr. 132, No. 1, 1-54 (2004).

J. Denef and F. Loeser developed the theory of motivic integration on algebraic varieties defined over fields of characteristic \(0\) [Invent. Math. 135, 201–232 (1999; Zbl 0928.14004) and Compos. Math. 131, 267–290 (2002; Zbl 1080.14001)]. The theory of motivic integration is generalized to formal schemes. In particular the boolean ring of measurable subsets, the motivic measure, the motivic integral are defined and studied. A theorem of change of variables for this integral is proved.

Reviewer: Gerhard Pfister (Kaiserslautern)

MSC:

14E18	Arcs and motivic integration
14D15	Formal methods and deformations in algebraic geometry
14A20	Generalizations (algebraic spaces, stacks)
14G10	Zeta functions and related questions in algebraic geometry (e.g., Birch-Swinnerton-Dyer conjecture)
14B05	Singularities in algebraic geometry

Keywords:

motivic integration; formal geometry

Citations:

Zbl 0928.14004; Zbl 1080.14001