Mathematical Sciences: Commutative Algebras

数学科学：交换代数

• 批准号: 9402015
• 负责人: Matam Murthy
• 金额: $ 7.5万
• 依托单位: University of Chicago
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1994
• 资助国家: 美国
• 起止时间: 1994-07-01 至 1997-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9402015&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Commutative; Algebras

9402015 Murthy The principal investigator will study the structure of projective modules and efficient generation of modules over affine algebras. He will continue his work on finding obstructions to splitting of projective modules and efficient generation of ideals, analogous to obstruction theory for sections of vector bundles in topology. Some of the ingredients for these obstructions are Chow groups. Other invariants have to be explored. The tools used are from intersection theory, algebraic K-theory, and standard commutative algebra. 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.

9402015 Murthy 首席研究员将研究射影模的结构以及仿射代数上模的高效生成。 他将继续致力于寻找射影模分裂和有效生成理想的障碍，类似于拓扑中矢量丛部分的障碍理论。 这些障碍的部分成分是松狮群体。 必须探索其他不变量。 使用的工具来自交集理论、代数 K 理论和标准交换代数。 这项研究涉及交换代数和代数几何中的许多问题。 代数几何研究多项式方程族的解。 人们可以研究解集的几何形状，也可以通过研究解集上形成所谓交换环的某些函数来用代数方法解决问题。 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。