Motivic Stack Inertia of Moduli Spaces of Curves, Variation of Periods and Multiple Zeta Values in Genus 0 and 1

本计画的目的是从动机的观点来研究曲线模空间情形下的堆叠惯性。我们的框架是两个折叠，一方面的Grothendieck-Teichmüller理论提供了一个丰富的和计算的双框架与算术和motivic方面;另一方面，最近Morel Voevodsky motivic同伦理论适应Deligne-Mumford堆栈提供了一个方便的类别的研究堆栈惯性。我们的研究是更精确地驱动应用程序的多个Zeta值在属一。它从考虑堆栈结构特殊性的动机范畴的定义，到可以与亏格为零的动机填充-洗牌关系相比较的新惯性关系的计算。通过Grothendieck-Teichmüller理论的两个方面，该项目扩展并依赖于最近的发展，即考虑堆栈惯性作为算术几何中的一个新的关键成分，同伦理论在动机论基础上的复兴。从这个SPP的角度来看，这项研究可以被视为经典算术几何和A^1-同伦理论之间的双向联系，双方都有新的发展，因此肯定会受益于与该计划其他参与者的交流。

The goal of this project is to study the stack inertia in the case of moduli spaces of curves from a motivic point of view. Our framework is two folds, with on one hand the Grothendieck-Teichmüller theory providing a rich and computational dual-framework with arithmetic and motivic sides; and on other hand the recent Morel-Voevodsky motivic homotopy theory adapted to Deligne-Mumford stacks providing a convenient category for the study of stack inertia. Our study is more precisely driven by applications to Multiple Zeta Values in genus one. It goes from the definition of a motivic category that takes into account the specificities of the stack structure, to the computation of new inertia relations that can be compared with the motivic stuffle-shuffle relation from genus zero.Through the two sides of Grothendieck-Teichmüller theory, this project extends and relies on very recent developments which are the consideration of stack inertia as a new key ingredient in Arithmetic Geometry, and the revival of Homotopy Theory in the foundation of Motivic theory. From the point of view of this SPP, this study can been seen as a two ways connection between classical Arithmetic Geometry and A^1-homotopy theory with new developments in both sides, and as such will certainly benefit from exchanges with other participants from the Programme.