Nonstandard Point Counting for Algebraic Varieties
Nonstandard Point Counting for Algebraic Varieties
复制标题
代数簇的非标准点计数
DOI：
10.1080/00927872.2012.737074
复制
发表时间：
2013
影响因子：
0.7
通讯作者：
Nobuyoshi
中科院分区：
文献类型：
--
作者：
Takahashi;Nobuyoshi
对于一个域上的变量，我们定义了在有序域中有值的动机测度，在有限域上使用点计数，并对超滤波器取极限。讨论了这些措施的一些性质和有关问题。我们通过计算周期点来定义代数动力系统的类似度量，并解释如何使用它们来证明某些陈述，例如动机zeta函数的非合理性。
For varieties over a fieldk, we define motivic measures with values in ordered fields, using point counting over finite fields and taking the limits with respect to ultrafilters. Some properties and problems related to such measures are discussed. We define similar measures for algebraic dynamical systems by counting periodic points, and explain how they can be used to prove certain statements, such as the non-rationality of a motivic zeta function.