1,362 research outputs found
Motivic integration and the Grothendieck group of pseudo-finite fields
We survey our recent work on an extension of the theory of motivic
integration, called arithmetic motivic integration. We developed this theory to
understand how p-adic integrals of a very general type depend on p.Comment: 11 page
Character sums associated to finite Coxeter groups
We prove a character sum identity for Coxeter arrangements which is a finite
field analogue of Macdonald's conjecture proved by Opdam.Comment: 20 pages, to appear in Transactions of the A.M.
Lefschetz numbers of iterates of the monodromy and truncated arcs
We express the Lefschetz number of iterates of the monodromy of a function on
a smooth complex algebraic variety in terms of the Euler characteristic of a
space of truncated arcs.Comment: 10 page
Definable sets, motives and p-adic integrals
We associate canonical virtual motives to definable sets over a field of
characteristic zero. We use this construction to show that very general p-adic
integrals are canonically interpolated by motivic ones.Comment: 45 page
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