Stacks Project Expository Collection

A collection of expository articles on modern topics in algebraic geometry, focusing on the geometry of algebraic spaces and stacks.

SPEC collects expository articles on the geometry of algebraic spaces and stacks. The articles bring researchers up to speed on recent developments and include detailed accounts in modern language of many results previously unavailable or only implicit in the literature, and where applicable use the Stacks project for preliminary material.The Stacks Project Expository Collection (SPEC) compiles expository articles in advanced algebraic geometry, intended to bring graduate students and researchers up to speed on recent developments in the geometry of algebraic spaces and algebraic stacks. The articles in the text make explicit in modern language many results, proofs, and examples that were previously only implicit, incomplete, or expressed in classical terms in the literature. Where applicable this is done by explicitly referring to the Stacks project for preliminary results. Topics include the construction and properties of important moduli problems in algebraic geometry (such as the Deligne–Mumford compactification of the moduli of curves, the Picard functor, or moduli of semistable vector bundles and sheaves), and arithmetic questions for fields and algebraic spaces.