Motivic stable homotopy groups

动机稳定同伦群

• 批准号: 1202213
• 负责人: Daniel Isaksen
• 金额: $ 11.15万
• 依托单位: Wayne State University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2012
• 资助国家: 美国
• 起止时间: 2012-08-15 至 2016-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1202213&HistoricalAwards=false
• 关键词: Motivic; stable; homotopy; groups

AbstractAward: DMS 1202213, Principal Investigator: Daniel C. IsaksenThe PI will carry out computations in motivic homotopy theory, i.e., the homotopy theory of algebraic varieties. The main point of motivic homotopy theory is to import the powerful methods of homotopy theory from topology to algebraic geometry. The PI would like to turn this relationship around by using results from algebraic geometry to discover new information about classical homotopy theory. For example, the PI has used motivic homotopy theory over C to completely reconstruct the classical 2-complete Adams-Novikov spectral sequence in a large range. Similarly, motivic computations over R have revealed new information about equivariant stable homotopy theory. Specifically, the PI is interested in the motivic version of the Adams spectral sequence, with base field R or C, where thorough computations are possible.Homotopy theory is a technique for studying geometric objects up to certain kinds of deformations. Homotopical approaches often allow for concrete calculations that are otherwise inaccessible. Computations of stable homotopy groups have been a major topic of research in topology since the middle of the 20th century. Although tremendous progress has been made, much remains unknown. In the 1990's, Fabien Morel and Vladimir Voevodsky developed motivic homotopy theory. In analogy to classical homotopy theory, motivic homotopy theory allows us to study algebraic objects up to certain kinds of deformations. Their goal was to import the techniques of homotopy theory into the realm of algebra. The PI's goal is the reverse: to use algebraic results to obtain new information about classical homotopy theory.

Abstractaward：DMS 1202213，主要研究者：Daniel C. Isaksenthe Pi将在动机同义理论（即代数品种的同型理论）中进行计算。 动机同义理论的重点是将强大的同质理论方法从拓扑到代数几何导入强大的方法。 PI希望通过使用代数几何形状的结果来发现有关经典同型理论的新信息，从而改变了这种关系。 例如，PI在C上使用了动机同义理论来完全重建大范围内经典的2个完整的Adams-Novikov光谱序列。 同样，对R的动机计算也揭示了有关稳定同义理论的新信息。具体而言，PI对ADAMS光谱序列的动机版本感兴趣，其基本场R或C，其中可能是彻底的计算。HOSOPOPY理论是一种研究几何学对象的技术，直到某些形式的变形。 同位方法通常允许进行原本无法访问的具体计算。 自20世纪中叶以来，稳定同质组的计算一直是拓扑研究的主要主题。 尽管已经取得了巨大进展，但仍然未知。 在1990年代，Fabien Morel和Vladimir Voevodsky开发了动机同义理论。 与古典同义理论相比，动机同义理论使我们能够研究代数对象，直到某些变形。 他们的目标是将同义理论的技术导入代数领域。 PI的目标是相反：使用代数结果获取有关经典同型理论的新信息。