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Constructible motivic functions and motivic integration
We introduce a direct image formalism for constructible motivic functions. One deduces a very general version of motivic integration for which a change of variables theorem is proved. TheseExpand
Fields with analytic structure
We present a unifying theory of fields with certain classes of analytic functions, called fields with analytic structure. Both real closed fields and Henselian valued fields are considered. For realExpand
Constructible exponential functions, motivic Fourier transform and transfer principle
We introduce spaces of exponential constructible functions in the motivic setting for which we construct direct image functors in the absolute and relative settings. This allows us to define aExpand
Igusa and Denef-Sperber conjectures on nondegenerate $p$-adic exponential sums
We prove the intersection of Igusa's Conjecture of [Igusa, J., "Lectures on forms of higher degree", Lect. math. phys., Springer-Verlag, 59 (1978)] and the Denef - Sperber Conjecture of [Denef, J.Expand
Definable equivalence relations and zeta functions of groups
The authors wish to thank Thomas Rohwer, Deirdre Haskell, Dugald Macpherson and Elisabeth Bouscaren for their comments on earlier drafts of this work, Martin Hils for suggesting that the proof couldExpand
Analytic cell decomposition and analytic motivic integration
Abstract The main results of this paper are a Cell Decomposition Theorem for Henselian valued fields with analytic structure in an analytic Denef–Pas language, and its application to analytic motivicExpand
Quantifier elimination in ordered abelian groups
We give a new proof of quantifier elimination in the theory of all ordered abelian groups in a suitable language. More precisely, this is only "quantifier elimination relative to ordered sets" in theExpand
Motivic integration in all residue field characteristics for Henselian discretely valued fields of characteristic zero
We extend the formalism and results on motivic integration from ["Constructible motivic functions and motivic integration", Invent. Math., Volume 173, (2008) 23-121] to mixed characteristicExpand
Transfer Principle for the Fundamental Lemma
The purpose of this paper is to explain how the identities of various fundamental lemmas fall within the scope of the transfer principle, a general result that allows to transfer theorems aboutExpand
Approximations and Lipschitz continuity in p-adic semi-algebraic and subanalytic geometry
It is known that a p-adic, locally Lipschitz continuous semi-algebraic function, is piecewise Lipschitz continuous, where finitely many pieces suffice and the pieces can be taken semi-algebraic. WeExpand