Intersection Multiplicity, Canonical Element & Related Problems in Algebra

交集重数、规范元素

• 批准号: 9406863
• 负责人: Sankar Dutta
• 金额: $ 6万
• 依托单位: University of Illinois at Urbana-Champaign
• 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: 1994-06-01 至 1999-05-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9406863&HistoricalAwards=false
• 关键词: Intersection; Multiplicity; Canonical; Element; &amp

This award supports work on two sets of major problems in commutative algebra. The principal investigator will work on Serre's conjecture on interesection multiplicity of modules and Chow groups of a complete ramified regular local ring. He will also work on the canonical element conjecture of Hochster and related problems. 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.

该奖项支持对交换代数中两组主要问题的研究。主要研究者将研究Serre关于完全分支正则局部环的模和Chow群相交多重性的猜想。他还将研究霍赫斯特的正则元猜想及相关问题。本研究涉及交换代数和代数几何中的若干问题。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解决问题，这些函数形成了所谓的交换环。这种对偶视角在交换代数和代数几何之间建立了紧密的联系。