Homological Conjectures in Commutative Algebra: A Conference in Honor of Paul C. Roberts

交换代数中的同调猜想：纪念 Paul C. Roberts 的会议

• 批准号: 0555525
• 负责人: Melvin Hochster
• 金额: $ 2万
• 依托单位: Regents of the University of Michigan - Ann Arbor
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2006
• 资助国家: 美国
• 起止时间: 2006-03-15 至 2008-02-29
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0555525&HistoricalAwards=false
• 关键词: Homological; Conjectures; Commutative; Algebra; Conference

This conference, which will occur at the same time as the sixtieth birthday of Paul Roberts, will deal with areas of commutative algebra and algebraic geometry related to his work, including the local homological behavior of commutative Noetherian rings, intersection theory, and K-theory. Of particular note is the application, pioneered by Roberts, of the theory of local Chern classes developed by Baum, Fulton, and MacPherson to the solution of long standing open questions in commutative algebra. These include M. Auslander's zerodivisor conjecture, the new intersection conjecture of Peskine and Szpiro, and Serre's conjecture on the vanishing of intersection multiplicities. Many other problems, such as the direct summand conjecture, remain to be solved.The participation of graduate students and recent Ph.D.s will be strongly encouraged, and open questions will be emphasized. The kinds of questions that will be considered may be thought of as follows. When one has many equations in many unknowns, one can think of the solutions algebraically, by forming an abstract system called a ring in which the equations are forced to hold, or geometrically, as a set that is contained in a possibly high dimensional space. The latter construction generalizes the notion of graphing an equation. When one has information about two solution sets, one wants to understand their intersection: the common solutions of both sets of equations. In particular, its dimension, which represents the number of degrees of freedom one has in choosing a solution, is of great interest. Many of the questions considered can be thought of as follows: given algebraic information about two solution sets, e.g., special properties of the corresponding rings, what quantitative and qualitative conclusions can one reach about the intersection? A major focus of the conference will be on very subtle and deep theorems and conjectures in this area.

这次会议，这将发生在同一时间作为六十岁生日的保罗罗伯茨，将处理领域的交换代数和代数几何有关他的工作，包括当地的同调行为的交换诺特环，交叉理论和K理论。 特别值得注意的是应用程序，开创了罗伯茨，理论的地方陈省身类开发的鲍姆，富尔顿，和麦克弗森的解决长期悬而未决的问题交换代数。其中包括M。Auslander的零因子猜想，Peskine和Szpiro的新交集猜想，以及Serre关于交集重数消失的猜想。 许多其他问题，如直和猜想，仍有待解决。研究生和最近的博士生的参与将受到强烈鼓励，并将强调开放性问题。 将被考虑的各种问题可以被认为是如下。 当一个人有许多未知数的许多方程时，他可以用代数的方法来思考解，通过形成一个抽象的系统，称为环，其中方程被迫保持不变，或者用几何的方法来思考解，作为一个可能包含在高维空间中的集合。后一种构造概括了绘制方程的概念。 当一个人有关于两个解集的信息时，他想了解它们的交集：两组方程的公共解。特别是，它的尺寸，这代表了自由度的数量在选择一个解决方案，是非常感兴趣的。考虑的许多问题可以考虑如下：给定关于两个解集的代数信息，例如，特殊性质的相应环，什么定量和定性的结论可以达到的交集？ 会议的一个主要重点将是在这一领域非常微妙和深刻的定理和理论。