Homological and Homotopical Algebra

同调和同伦代数

• 批准号: 1817931
• 金额: --
• 依托单位: Swansea University
• 依托单位国家: 英国
• 项目类别: Studentship
• 财政年份: 2016
• 资助国家: 英国
• 起止时间: 2016 至 无数据
• 项目状态: 已结题
• 来源: https://gtr.ukri.org/projects?ref=studentship-1817931
• 关键词: Homological; Homotopical; Algebra

Algebra & Geometry. Homological and homotopical algebra is a spectacular area of Mathematics with many applications within and around mathematics. One of the ingenious discoveries were made by V Voevodsky, who was awarded the Fields medal in 2002. His work lead top solution of a number of longstanding problems with far reaching implications. Very recently, Dr G Garkusha and I Panin have accomplished a programme of Voevodsky, which began in 2001. G Garkusha and I Panin use enriched motivic homotopy theory. The project is to explore and develop further aspects of the enriched homotopy theory and enriched homological algebra which is of major importance in Garkusha-Panin's theory. Applications are expected in motivic homotopy theory, ring and module theory, homological algebra..

代数与几何。同调和同伦代数是数学中一个引人注目的领域，在数学内部和数学周围有许多应用。其中一项巧妙的发现是V·沃沃茨基做出的，他在2002年被授予菲尔兹奖。他的工作引领了一系列具有深远影响的长期问题的顶级解决方案。最近，G Garkusha博士和I Panin完成了始于2001年的Voevodsky方案。G Garkusha和I Panin使用了丰富的基元同伦理论。这个项目是为了进一步探索和发展丰富的同伦理论和丰富的同调代数，这在Garkusha-Panin的理论中是重要的。期望在动机同伦理论、环与模理论、同调代数等方面得到应用。

项目成果

Model Theory of Modules, Algebras and Categories

模、代数和范畴的模型论

• DOI: 10.1090/conm/730/14708
• 发表时间: 2019
• 作者: Garkusha G

Recollements for derived categories of enriched functors and triangulated categories of motives

对丰富函子的派生类别和动机三角类别的建议

• DOI: 10.1016/j.jalgebra.2021.09.020
• 发表时间: 2022
• 期刊: Journal of Algebra
• 影响因子: 0.9
• 作者: Garkusha G