Enriched motivic homotopy theory

丰富的动机同伦理论

• 批准号: EP/J013064/1
• 负责人: Grigory Garkusha
• 金额: $ 2.83万
• 依托单位: Swansea University
• 依托单位国家: 英国
• 项目类别: Research Grant
• 财政年份: 2012
• 资助国家: 英国
• 起止时间: 2012 至 无数据
• 项目状态: 已结题
• 来源: https://gtr.ukri.org/projects?ref=EP%2FJ013064%2F1
• 关键词: Enriched; motivic; homotopy; theory

The versatility of motivic homotopy theory and its associated range of cohomological techniques has made it an important branch of mathematics. Recently there have been several fundamental developments which have been used to solve a number of longstanding problems. The new strategically important developments are related to the names of V. Voevodsky (Fields Medal 2002), M. Rost, A. Suslin, I. Panin, M. Levine, F. Morel.The principal aim of this project is to investigate enriched motivic homotopy theory. It is hoped that its study will shed light on some classical problems in A^1-topology. We propose to use its methods to construct various triangulated categories of motives, one of the central objects of study in modern A^1-topology. We believe that these constructions will have important computational advantages. The homotopy-theoretic outlook that we develop is likely to be useful in other areas of mathematics such as algebraic topology and non-commutative geometry.The research will be undertaken in the Department of Mathematics, Swansea University.

动机同伦理论及其相关的上同调技术的多功能性使其成为数学的一个重要分支。最近出现了一些基础性的发展，这些发展已被用来解决许多长期存在的问题。新的具有重要战略意义的进展与 V. Voevodsky（2002 年菲尔兹奖）、M. Rost、A. Suslin、I. Panin、M. Levine、F. Morel 的名字有关。该项目的主要目的是研究丰富的动机同伦理论。希望其研究能够阐明 A^1 拓扑中的一些经典问题。我们建议使用其方法来构建各种动机的三角类别，这是现代 A^1 拓扑研究的中心对象之一。我们相信这些结构将具有重要的计算优势。我们开发的同伦理论观点可能在其他数学领域有用，例如代数拓扑和非交换几何。这项研究将在斯旺西大学数学系进行。

项目成果

ON THE MOTIVIC SPECTRAL SEQUENCE

关于动机谱序列

• DOI: 10.1017/s1474748015000419
• 发表时间: 2015
• 期刊: Journal of the Institute of Mathematics of Jussieu
• 影响因子: 0.9
• 作者: Garkusha G