Depth Properties of Modules Over Local Rings

本环上模块的深度特性

• 批准号: 9801309
• 负责人: Roger Wiegand
• 金额: $ 5.91万
• 依托单位: University of Nebraska-Lincoln
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1998
• 资助国家: 美国
• 起止时间: 1998-07-01 至 2001-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9801309&HistoricalAwards=false
• 关键词: Depth; Properties; Modules; Over; Local

WIEGAND98-01309This award supports research in homological and commutative algebra. Three related topics will be investigated: homological theory of local rings, representation theory of modules over local tings and Picard groups of algebraic varieties over field that are not algebraically closed.Commutative algebra, among other things, studies the solutions of polynomial or power series equations by forming an algebraic object, called a ring, which consists of the 'generic' solutions. The algebraic properties of these generic solutions then give insight into the geometric and algebraic nature of the equations. The field combines techniques from a number of other areas including combinatorics, topology, and analysis.

WIEGAND 98 - 01309该奖项支持同调和交换代数的研究。 三个相关的主题将被调查：同调理论的局部环，表示理论的模局部环和皮卡德群的代数簇域是不代数封闭的。交换代数，除其他事项外，研究解决方案的多项式或幂级数方程形成一个代数对象，称为一个环，其中包括'通用'的解决方案。 这些通用的解决方案的代数性质，然后洞察到几何和代数性质的方程。 该领域结合了许多其他领域的技术，包括组合学，拓扑学和分析。