Constructive Module Theory for Algebras

上同调是一个高度抽象但非常强大的工具。要将它应用于特定问题，需要对深奥的对象进行复杂的计算。该项目将代表着坎农和其他人正在进行的一项长期研究计划中的重要一步，该计划旨在开发利用代数和几何中强大但深度抽象的概念的计算方法。这些问题的解决将引起人们的极大兴趣，并在数学的几个分支中得到应用，包括代数几何和代数拓扑学。它既用于获得理论见解，也用于解决具体问题，例如确定一个方程(如x^3+y^9=z^2)是否有整数解。

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.