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.

动机同伦理论的多功能性及其相关的一系列上同调技巧使其成为数学的一个重要分支。最近有几个基本的发展，已被用来解决一些长期存在的问题。新的具有重要战略意义的发展与V. Voevodsky（2002年菲尔兹奖），M。Rost，A.苏斯林岛Panin，M. Levine，F.莫雷尔。该项目的主要目的是研究丰富的动机同伦理论。希望它的研究能对A^1-拓扑学中的一些经典问题有所启发。我们建议使用它的方法来构造各种三角化的动机范畴，这是现代A^1-拓扑学的中心研究对象之一。我们相信这些构造将具有重要的计算优势。同伦理论的前景，我们开发的是可能是有用的数学的其他领域，如代数拓扑和非交换几何。这项研究将在数学系，斯旺西大学进行。

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