Derived categories and their applications, especially in K-theory, topology and algebraic geometry

派生范畴及其应用，特别是在 K 理论、拓扑和代数几何中

• 批准号: DP0343239
• 负责人: Prof Amnon Neeman
• 金额: $ 45.21万
• 依托单位: The Australian National University
• 依托单位国家: 澳大利亚
• 项目类别: Discovery Projects
• 财政年份: 2003
• 资助国家: 澳大利亚
• 起止时间: 2003-01-01 至 2008-12-31
• 项目状态: 已结题
• 来源: https://dataportal.arc.gov.au/RGS/Web/Grants/DP0343239
• 关键词: Derived; categories; their; applications; especially

Algebraic geometry, topology and algebraic K-theory are mathematical disciplines that study different aspects of geometry. In all these areas of study, derived categories have proved to be powerful tools. This project aims to use derived categories to advance our understanding of geometry. Involved are some of the main open questions in geometry from the second half of the twentieth century. The research is being nominated for the Complex/Intelligent Systems Priority Area. Geometry is relevant in two ways. Secure and/or error correcting codes are often based on algebraic geometry. And modelling concurrency problems involves homotopy theory.

代数几何，拓扑和代数K理论是研究几何学不同方面的数学学科。在所有这些研究领域，衍生类别已被证明是强大的工具。该项目旨在使用派生类别来提高我们对几何形状的理解。涉及的是二十世纪下半叶的几何形状中的一些主要开放问题。 该研究正在提名复杂/智能系统优先领域。几何以两种方式相关。安全和/或错误纠正代码通常基于代数几何形状。建模并发问题涉及同义理论。