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Download as PDF; Printable version; In other projects ... The Stacks Project is an open source collaborative mathematics textbook writing project with the aim to ...
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.
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.
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.
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Let ,,, be as in the above example. But this time let denote the scheme obtained by gluing , along the isomorphism given by . [3] So, geometrically, is obtained by identifying two parallel lines except the origin; i.e., it is an affine line with the doubled origin.
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