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The Stacks Project is an open source collaborative mathematics textbook writing project with the aim to cover "algebraic stacks and the algebraic geometry needed to define them".
Terminology: The definition given here is the one used by the first edition of EGA and the Stacks Project. In the second edition of EGA constructible sets (according to the definition above) are called "globally constructible" while the word "constructible" is reserved for what are called locally constructible above.
The Stacks Project authors. "6.11 Stalks". The Stacks Project authors. "6.27 Skyscraper sheaves and stalks". Goresky, Mark. "Introduction to Perverse Sheaves" (PDF). Institute for Advanced Study. Kiran Kedlaya. 18.726 Algebraic Geometry (LEC # 3 - 5 Sheaves)Spring 2009. Massachusetts Institute of Technology: MIT OpenCourseWare Creative Commons ...
A PDF file is organized using ASCII characters, except for certain elements that may have binary content. The file starts with a header containing a magic number (as a readable string) and the version of the format, for example %PDF-1.7. The format is a subset of a COS ("Carousel" Object Structure) format. [23]
An algebraic stack or Artin stack is a stack in groupoids X over the fppf site such that the diagonal map of X is representable and there exists a smooth surjection from (the stack associated to) a scheme to X.
In mathematics, an algebraic stack is a vast generalization of algebraic spaces, or schemes, which are foundational for studying moduli theory.Many moduli spaces are constructed using techniques specific to algebraic stacks, such as Artin's representability theorem, which is used to construct the moduli space of pointed algebraic curves, and the moduli stack of elliptic curves.
Higher Topos Theory covers two related topics: ∞-categories and ∞-topoi (which are a special case of the former). The first five of the book's seven chapters comprise a rigorous development of general ∞-category theory in the language of quasicategories, a special class of simplicial set which acts as a model for ∞-categories.
For example, if denotes the moduli stack of rank-n vector bundles, then there is a presentation given by the trivial bundle over (). A quasi-affine morphism between algebraic stacks is a morphism that factorizes as a quasi-compact open immersion followed by an affine morphism .