# Germs of arcs on singular algebraic varieties and motivic integration

@article{Denef1999GermsOA, title={Germs of arcs on singular algebraic varieties and motivic integration}, author={Jan Denef and François Loeser}, journal={Inventiones mathematicae}, year={1999}, volume={135}, pages={201-232} }

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 analogue of the rationality of the Poincare series associated to p-adic points on a p-adic variety. The main tools which are used are semi-algebraic geometry in spaces of power series and motivic integration (a notion introduced by M. Kontsevich). In particular we develop the theory of motivic integration for semi…

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