Integration in algebraically closed valued fields

Abstract

The first two steps of the construction of motivic integration in the fundamental work of Hrushovski and Kazhdan have been presented in arXiv:1006.2467v1. In this paper we present the final third step. As in arXiv:1006.2467v1, we limit our attention to the theory of algebraically closed valued fields of pure characteristic 0 expanded by a (VF, Γ)-generated substructure S in the language L_{RV}. A canonical description of the kernel of the lifting map is obtained.

This new paper and arXiv:1006.2467v1 are the published version of the old paper. To appear in the Annals of Pure and Applied Logic

References in corpus (2)

• Transfer Principle for the Fundamental Lemma
• Motivic Poisson summation

Cited by in corpus (6)

• Quantifier elimination and minimality conditions in algebraically closed valued fields
• Fourier transform of the additive group in algebraically closed valued fields
• Additive invariants in o-minimal valued fields
• Special transformations in algebraically closed valued fields
• Generalized Euler characteristic in power-bounded T-convex valued fields
• Integration in algebraically closed valued fields with sections