图式Grothendieck环与动机理性
Schemic Grothendieck rings and motivic rationality
摘要：
我们提出了一个合适的替代品的经典Grothendieck环的代数闭域，其中任何准射影概形表示，而保持其非约化结构。这产生了一个更微妙的不变量，称为图式格罗滕迪克环，在其中我们可以通过弧计划制定类似于Kontsevich的motivic积分的积分形式。鉴于其更多的函子性质，我们可以提出一个特征的证明的合理性的几何Igusa zeta级数的某些超曲面，从而推广了突破性的工作，motivic集成Denef和Loeser。该构造使用一阶公式和一些称为公式集的无穷版本。
英文摘要：
We propose a suitable substitute for the classical Grothendieck ring of an algebraically closed field, in which any quasi-projective scheme is represented, while maintaining its non-reduced structure. This yields a more subtle invariant, called the schemic Grothendieck ring, in which we can formulate a form of integration resembling Kontsevich's motivic integration via arc schemes. In view of its more functorial properties, we can present a characteristic-free proof of the rationality of the geometric Igusa zeta series for certain hypersurfaces, thus generalizing the ground-breaking work on motivic integration by Denef and Loeser. The construction uses first-order formulae, and some infinitary versions, called formularies.
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