Mathematical Sciences: Topics in Commutative Algebra

数学科学：交换代数主题

• 批准号: 9502708
• 负责人: Christel Rotthaus
• 金额: $ 9.56万
• 依托单位: Michigan State University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1995
• 资助国家: 美国
• 起止时间: 1995-06-01 至 1999-05-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9502708&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Topics; Commutative; Algebra

This project addresses three different areas. The first is concerned with various topics in connection with the construction of local noetherian rings. The principal investigator will consider formal fibers and birational extensions, questions concerning rings with low dimensional formal fibers, and a closure operation for local morphisms of local excellent rings. The second part deals with a problem on divisor class groups in rings with the approximation property while the third part is concerned with a question on local-global annihilation of local cohomology. This research is concerned with a number of questions in commutative algebra and algebraic geometry. Algebraic geometry studies solutions of families of polynomial equations. One can either study the geometry of the solution set or approach problems algebraically by investigating certain functions on the solution set that form what is called a commutative ring. This dual perspective creates a close connection between commutative algebra and algebraic geometry.

这个项目涉及三个不同的领域。第一个是关于局部Notherian环的构造的各种主题。主要的研究人员将考虑形式纤维和双射扩张，关于具有低维形式纤维的环的问题，以及局部优秀环的局部态射的闭包运算。第二部分讨论了环中具有逼近性质的除子类群的问题，第三部分讨论了局部上同调的局部-整体零化问题。这项研究涉及到交换代数和代数几何中的一些问题。代数几何研究多项式方程族的解。人们既可以研究解集的几何，也可以通过研究解集上的某些函数来代数地处理问题，这些函数构成了所谓的交换环。这种双重视角在交换代数和代数几何之间建立了紧密的联系。