论文标题
在特殊刚性品种和动机积分身份猜想上的动机融合
Motivic integration on special rigid varieties and the motivic integral identity conjecture
论文作者
论文摘要
我们在本文中证明了Kontsevich的原始版本和Soibelman的动机积分身份猜想，通过为特殊刚性品种的e象动机整合开发新颖的框架，以构想正式功能。这一理论是基于我们最近在特殊正式方案领域中对模棱两可的动机融合的研究。我们方法的核心要素在于证明给定平滑刚性品种的两个形式模型可以由第三个正式模型主导。值得注意的是，Bosch，Lütkebohmert和Raynaud在1993年获得了准混合刚性品种的类似断言。因此，我们为特殊平滑的刚性品种建立了动机量的概念，以确保独立于其模型的选择。我们证明，这种动机可以扩展到从特殊的平滑刚性品种的特定色态环到经典的Grothendieck戒指的同态。此外，我们发达的动机量展示了Fubini-Type属性，该属性恢复了Nicaise和Payne的动机Fubini定理，用于热带化图。
We prove in this paper the original version of Kontsevich and Soibelman's motivic integral identity conjecture for formal functions by developing a novel framework for equivariant motivic integration on special rigid varieties. This theory is built upon our recent research on equivariant motivic integration within the realm of special formal schemes. The central element of our approach lies in demonstrating that two formal models of a given smooth rigid variety can be dominated by a third formal model. Notably, a similar assertion for quasi-compact rigid varieties was obtained by Bosch, Lütkebohmert, and Raynaud in 1993. Consequently, we establish a concept of motivic volume for a special smooth rigid variety, ensuring independence from the selection of its models. We demonstrate that this motivic volume can be extended to a homomorphism from a certain Grothendieck ring of special smooth rigid varieties to the classical Grothendieck ring of varieties. Moreover, our developed motivic volume exhibits a Fubini-type property, which recovers Nicaise and Payne's motivic Fubini theorem for the tropicalization map.
