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

Denef, J.

Loeser, F.

English

arXiv

Motivic integration is a powerful technique to prove that certain quantities  associated to algebraic varieties are birational invariants or are independent of  a chosen resolution of singularities. 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. Quanti  er elimination plays a key role

Motivic integration and the Grothendieck group of pseudo-finite fields

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