The Stacks Project in Algebraic Geometry

该项目旨在继续Stacks项目的主要研究者的工作，Stacks项目是一个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，从基本代数和集合论开始，直到代数堆栈理论。Stacks项目为文献提供了指针，并制定了自然问题，以这种方式缩小了研究生教育和当前研究之间的差距。该项目的网站（http：//stacks.math.columbia.edu/）提供了几种与材料互动的方式，以及一个对材料发表评论和提出问题的系统。 该项目还包括一个研讨会，参与者在数学和进一步开发堆栈项目的网站上工作。代数堆栈被广泛使用，特别是用于思考模空间，并且是当今代数几何中最重要的工具之一。一方面，Stacks项目文本将澄清并明确阐述文献中的“民俗学”和旧成果，另一方面，最近的方法和发现将用于基础成果的阐述。在这些活动的过程中，数学问题自然会出现;主要研究者打算研究这些问题，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研究算术代数几何中的其他问题，无论是独立还是与博士后同事和研究生共同研究。该奖项由代数和数论计划以及基础设施计划共同资助。

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.