4 papers
Bounded integral and motivic Milnor fiber
Arthur Forey, Yimu Yin
We construct a new motivic integration morphism, the so-call bounded integral, that interpolates both the integration morphisms with and without volume forms of Hrushovski and Kazh…
Uniform Yomdin-Gromov parametrizations and points of bounded height in valued fields
Raf Cluckers, Arthur Forey, François Loeser
We prove a uniform version of non-Archimedean Yomdin-Gromov parametrizations in a definable context with algebraic Skolem functions in the residue field. The parametrization result…
A motivic local Cauchy-Crofton formula
Arthur Forey
In this note, we establish a version of the local Cauchy-Crofton formula for definable sets in Henselian discretely valued fields of characteristic zero. It allows to compute the m…
Virtual rigid motives of semi-algebraic sets
Arthur Forey
Let be a field of characteristic zero containing all roots of unity and . We build a ring morphism from the Grothendieck group of semi-algebraic sets over to the…