Characteristic p Methods in Commutative Algebra

交换代数中的特征 p 方法

• 批准号: 9731512
• 负责人: Craig Huneke
• 金额: $ 7.17万
• 依托单位: Purdue Research Foundation
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1998
• 资助国家: 美国
• 起止时间: 1998-06-01 至 1999-02-16
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9731512&HistoricalAwards=false
• 关键词: Characteristic; Methods; Commutative; Algebra

HUNEKE, 97-31512 This award supports research in commutative algebra and algebraic geometry. The principal investigator will continue to investigate a group of long standing questions centered around the process of reduction to positive characteristic, especially in regard to the developing theory of tight closure. Particular emphasis will be placed on the relationship between tight closure, reduction to positive characteristic, and vanishing theorems in algebraic geometry such as the Kodaira vanishing theorem. Closely related work will be done on questions concerning uniform bounds in Noetherian rings, and in particular on the uniform Artin-Rees conjectures. This is research in the closely related fields of commutative algebra and algebraic geometry. In essence these fields are quite similar to the 19th century study of equations and their solutions. The relationship between algebraic equations, such as polynomial equations, and geometry goes back at least to Descartes and the idea of coordinatizing the plane. Commutative algebra studies the solutions of such 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.

胡内克，97-31512 该奖项支持交换代数和代数几何的研究。 主要研究者将继续研究一组长期存在的问题，这些问题围绕着还原为阳性特征的过程，特别是关于紧密闭合理论的发展。 特别强调将放在紧封闭之间的关系，减少积极的特点，并消失定理代数几何，如科代拉消失定理。 密切相关的工作将做的问题，一致的边界在诺特环，特别是对统一的阿廷里斯结构。 这是在交换代数和代数几何密切相关的领域的研究。从本质上讲，这些领域与世纪对方程及其解的研究非常相似。 代数方程（如多项式方程）和几何之间的关系至少可以追溯到笛卡尔和平面坐标化的思想。 交换代数通过形成一个代数对象（称为环）来研究此类多项式或幂级数方程的解，该代数对象由“通用”解组成。 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。