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.

该项目旨在继续在堆栈项目上的主要研究者的工作，这是一本协作的在线开源教科书和代数几何学的参考作品。目的是从基本代数和设定理论开始，发展和记录代数几何学理论，并导致代数堆栈的理论。堆栈项目为文献提供了指示，并提出了自然问题，以此来缩小研究生教育与当前研究之间的差距。项目网站（http://stacks.math.columbia.edu/）提供了几种与材料互动的方法，以及一个在材料上留下评论和问题的系统。 该项目还涉及一个研讨会，参与者在数学上都在研究堆栈项目的网站。代数堆栈被广泛使用，尤其是用于思考模量空间，并且是当今代数几何学中最重要的工具之一。一方面，堆栈项目文本将澄清并清楚地阐述了文献中的“民间传说”和较旧的结果，另一方面，最新的方法和发现将用于阐明基本结果。在此类活动过程中，数学问题自然出现。首席研究人员打算研究这些内容，并与他人合作，回答它们并仔细记录答案。首席研究者还将继续研究算术代数几何学的其他问题，无论是独立和共同与博士后伙伴和研究生共同的问题。该奖项由代数理论计划和基础设施计划共同资助。