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

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.

### 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
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