45 research outputs found
Integration of positive constructible functions against Euler characteristic and dimension
Following recent work of R. Cluckers and F. Loeser [Fonctions constructible
et integration motivic I, C. R. Math. Acad. Sci. Paris 339 (2004) 411 - 416] on
motivic integration, we develop a direct image formalism for positive
constructible functions in the globally subanalytic context. This formalism is
generalized to arbitrary first-order logic models and is illustrated by several
examples on the p-adics, on the Presburger structure and on o-minimal
expansions of groups. Furthermore, within this formalism, we define the Radon
transform and prove the corresponding inversion formula.Comment: To appear in Journal of Pure and Applied Algebra; 8 page
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. These constructions are generalized to the
relative framework, in which we develop a relative version of motivic
integration. These results have been announced in math.AG/0403349 and
math.AG/0403350.
Main results and statements unchanged. Many minor slips corrected and some
details added.Comment: Final versio