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.
