Stacks Project Expository Collection

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.