The Stacks Project in Algebraic Geometry

代数几何中的 Stacks 项目

• 批准号: 1601160
• 负责人: Aise de Jong
• 金额: $ 25.66万
• 依托单位: Columbia University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2016
• 资助国家: 美国
• 起止时间: 2016-07-01 至 2021-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1601160&HistoricalAwards=false
• 关键词: Stacks; Project; Algebraic; Geometry

This project aims to continue the work of the principal investigator on the Stacks project, a collaborative online open source textbook and reference work on algebraic geometry. The goal is to develop and document the theory of algebraic geometry, starting from basic algebra and set theory and leading up to the theory of algebraic stacks. The Stacks project gives pointers to the literature and formulates natural questions, in this way closing the gap between graduate education and current research. The project website (http://stacks.math.columbia.edu/) provides several ways of interacting with the material, as well as a system to leave comments and questions on the material. This project also involves a workshop where participants work on both the mathematics and further developing the website of the Stacks project.Algebraic stacks are widely used, especially for thinking about moduli spaces, and are one of the most important tools in algebraic geometry today. On the one hand, the Stacks project text will clarify and give a clear exposition of "folklore" and older results in the literature, and on the other hand, recent methods and discoveries will be used in the exposition of foundational results. During the course of such activities, mathematical questions arise naturally; the principal investigator intends to study these and, in collaboration with others, answer them and carefully document the answers. The principal investigator will also continue to research other problems in arithmetic algebraic geometry, both independently and jointly with postdoctoral associates and graduate students. This award is co-funded by the Algebra and Number Theory program and the Infrastructure program.

该项目旨在继续 Stacks 项目首席研究员的工作，Stacks 项目是一本关于代数几何的协作在线开源教科书和参考书。目标是发展和记录代数几何理论，从基础代数和集合论开始，一直到代数栈理论。 Stacks 项目提供文献指导并提出自然问题，从而缩小研究生教育与当前研究之间的差距。该项目网站 (http://stacks.math.columbia.edu/) 提供了多种与材料交互的方式，以及对材料留下评论和问题的系统。 该项目还包括一个研讨会，参与者将致力于数学工作并进一步开发 Stacks 项目的网站。代数堆栈被广泛使用，特别是在思考模空间时，是当今代数几何中最重要的工具之一。一方面，Stacks项目文本将对文献中的“民间传说”和较早的结果进行澄清和清晰的阐述，另一方面，最新的方法和发现将用于对基础性结果的阐述。在这样的活动过程中，数学问题自然而然地出现了。首席研究员打算研究这些问题，并与其他人合作，回答这些问题并仔细记录答案。首席研究员还将继续独立或与博士后和研究生联合研究算术代数几何中的其他问题。该奖项由代数和数论项目以及基础设施项目共同资助。