Constructive Module Theory for Algebras

代数的构造模理论

• 批准号: DP1096599
• 负责人: Prof John Cannon
• 金额: $ 20.9万
• 依托单位: The University of Sydney
• 依托单位国家: 澳大利亚
• 项目类别: Discovery Projects
• 财政年份: 2010
• 资助国家: 澳大利亚
• 起止时间: 2010-04-08 至 2013-04-06
• 项目状态: 已结题
• 来源: https://dataportal.arc.gov.au/RGS/Web/Grants/DP1096599
• 关键词: Constructive; Module; Theory; Algebras

Cohomology is a highly abstract but very powerful tool. To apply it to particular problems, intricate calculations with abstruse objects are required. The project will represent an important step in a long-term research program being undertaken by Cannon and others to develop computational methods that exploit powerful but deeply abstract ideas in algebra and geometry. Solution of the problems will create considerable interest and find application in several branches of mathematics including algebraic geometry and algebraic topology. It will be used both to gain theoretical insight and also to solve concrete problems such as determining whether an equation such as x^3+y^9 = z^2 has a solution in integers.

上同调是一个非常抽象但非常强大的工具。为了将它应用于特定的问题，需要对深奥的对象进行复杂的计算。坎农和其他人正在进行一项长期研究计划，旨在开发利用代数和几何中强大但非常抽象的概念的计算方法，该项目将代表该计划的重要一步。这些问题的解决将引起相当大的兴趣，并在数学的几个分支中找到应用，包括代数几何和代数拓扑。它将用于获得理论洞察力，也用于解决具体问题，如确定方程，如x^3+y^9 = z^2是否有整数解。