Motivic homotopy theory for local quotient stacks

局部商栈的动机同伦理论

• 批准号: 405327720
• 负责人: Professor Dr. Jochen Heinloth
• 金额: --
• 依托单位: Forschungsgebiet Algebraische Geometrie und Arithmetik
• 依托单位国家: 德国
• 项目类别: Priority Programmes
• 财政年份: 2018
• 资助国家: 德国
• 起止时间: 2017-12-31 至 2021-12-31
• 项目状态: 已结题
• 来源: https://gepris.dfg.de/gepris/projekt/405327720?language=en
• 关键词: Motivic; homotopy; theory; local; quotient

To classify and study geometric objects that appear in continuous families in which some members admit a large set of symmetries, algebraic stacks have proven to be a powerful geometric tool. These objects are spaces in which the building blocks admit Symmetries. In this research project we construct and study algebraic invariants of these objects that can be obtained using methods from homotopy theory.The basis for our construction is the motivic homotopy theory introduced by Morel and Voevodsky for the study of algebraic and arithmetic varieties. We want to extend their thoery in a way that allows to obtain information on the geometry of a large class of algebraic stacks and remove previous technical restrictions.In many important examples the known geometric invariants of these objects turned out to have unexpectedly favorable properties and the origin of this behavior has not yet found a satisfactory explanation. We want to provide a class of fine invariants for these space and use them to obtain a better understanding of the observed unexpected behavior.

为了分类和研究出现在连续族中的几何对象，其中一些成员承认一个大的对称集，代数栈已被证明是一个强大的几何工具。这些对象是其中的构建块承认对称性的空间。在这个研究项目中，我们构造和研究这些对象的代数不变量，可以使用同伦理论的方法获得。我们构造的基础是由Morel和Voevodsky介绍的用于研究代数和算术簇的motivic同伦理论。我们希望扩展他们的理论，使之能够获得一个大类的代数stacks.In许多重要的例子中，这些对象的已知几何不变量的几何形状的信息和删除以前的技术限制原来有意想不到的有利性质和这种行为的起源尚未找到一个令人满意的解释。我们希望为这些空间提供一类精细的不变量，并使用它们来更好地理解所观察到的意外行为。