Germs of arcs on singular algebraic varieties and motivic integration
Germs of arcs on singular algebraic varieties and motivic integration
复制标题
奇异代数簇上的弧萌芽和动机积分
DOI：
10.1007/s002220050284
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发表时间：
1998
影响因子：
3.1
通讯作者：
F. Loeser
中科院分区：
文献类型：
--
作者：
J. Denef;F. Loeser
研究了奇异代数簇上的形式弧的概型及其在截断下的象。我们证明了这些图像的庞加莱系列的合理性结果，这是一个模拟的合理性的庞加莱系列相关联的p-adic点上的p-adic品种。主要的工具是半代数几何空间的幂级数和motivic整合（一个概念介绍了M。Kontsevich）。特别是，我们开发的理论motivic整合的半代数集的形式弧奇异代数簇，我们证明了一个变化的变量公式的双有理态射，我们证明了一个几何模拟的结果Oesterle。
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-algebraic sets of formal arcs on singular algebraic varieties, we prove a change of variable formula for birational morphisms and we prove a geometric analogue of a result of Oesterle.