We study the scheme of formal arcs on a singular algebraic variety and its images under
truncations. We prove a rationality result for the Poincare series of these images which is an …

We define motivic analogues of Igusa's local zeta functions. These functions take their
values in a Grothendieck group of Chow motives. They specialize to p-adic Igusa local zeta …

In this paper we introduce a new notion of weight structure (w) for a triangulated category C;
this notion is an important natural counterpart of the notion of t-structure. It allows extending …

Geometry on Arc Spaces of Algebraic Varieties Page 1 Geometry on Arc Spaces of Algebraic
Varieties Jan Denef and Fran<;ois Loeser Abstract. This paper is a survey on arc spaces, a …

Using the weak factorization theorem, we give a simple presentation for the value group of
the universal Euler characteristic with compact support for varieties of characteristic zero and …

This book combines foundational constructions in the theory of motives and results relating
motivic cohomology to more explicit constructions. Prerequisite for understanding the work is …

This book presents several basic techniques in algebraic geometry, group representations,
number theory, l-adic and standard cohomology, and modular forms. It explores how NX (p) …

This book casts the theory of periods of algebraic varieties in the natural setting of Madhav
Nori's abelian category of mixed motives. It develops Nori's approach to mixed motives from …

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 …

DEFINABLE SETS, MOTIVES AND p-ADIC INTEGRALS Introduction 0.1. Let X be a scheme,
reduced and separated, of finite type over Z. Page 1 JOURNAL OF THE AMERICAN …