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.

《The Stacks Project Expository Collection (SPEC)》是一本彙編了關於高等代數幾何的專題文章的書籍，旨在讓研究生和研究人員了解最新的代數空間和代數堆研究進展。這本書中的文章以現代語言明確地呈現了許多以前只有隱含、不完整或以古典術語表達的結果、證明和例子。在適用的情況下，這些文章明確地參考了《Stacks Project》中的初步結果。主題包括代數幾何中重要的模問題的構造和性質（例如Deligne-Mumford曲線模空間的緊致化、Picard函子或半穩定向量丛和層的模空間），以及關於域和代數空間的算術問題。