摘要翻译：
设f是维数为D的非奇异复代数簇上的正则函数。我们用嵌入分辨率证明了f的motivic zeta函数的一个公式。该公式是在Grothendieck环本身之上的，并专门针对Denef和Loeser在某一局部化上的公式。我们还证明了满足f=0的n-喷流空间可以划分为局部闭子集，这些子集同构于维数为dn/2的仿射空间的笛卡尔积。最后，我们看一下motivic zeta函数极点的结果。
---
英文标题：
《The motivic zeta function and its smallest poles》
---
作者：
Dirk Segers, Lise Van Proeyen, Willem Veys
---
最新提交年份：
2012
---
分类信息：

一级分类：Mathematics        数学
二级分类：Algebraic Geometry        代数几何
分类描述：Algebraic varieties, stacks, sheaves, schemes, moduli spaces, complex geometry, quantum cohomology
代数簇，叠，束，格式，模空间，复几何，量子上同调
--

---
英文摘要：
  Let f be a regular function on a nonsingular complex algebraic variety of dimension d. We prove a formula for the motivic zeta function of f in terms of an embedded resolution. This formula is over the Grothendieck ring itself, and specializes to the formula of Denef and Loeser over a certain localization. We also show that the space of n-jets satisfying f=0 can be partitioned into locally closed subsets which are isomorphic to a cartesian product of some variety with an affine space of dimension the round up of dn/2. Finally, we look at the consequences for the poles of the motivic zeta function.
---
PDF链接：
https://arxiv.org/pdf/0710.5911