| Description |
1 online resource (v, 120 pages) |
| Series |
Memoirs of the American Mathematical Society ; number 1282 |
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Memoirs of the American Mathematical Society ; no. 1282
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| Contents |
Cover -- Title page -- Chapter 1. Introduction -- 1.1. Overview of our approach -- 1.2. Organization and Main Results -- 1.3. Conventions and Notations -- Acknowledgments -- Chapter 2. Preliminaries on higher topos theory -- 2.1. The epi-mono factorization system -- 2.2. Grothendieck topologies -- 2.3. Sheaves on ı-categories of ı-topoi. -- 2.4. The (ı,2)-category of ı-topoi. -- Chapter 3. Local Homeomorphisms and Étale Maps of ı-Topoi -- 3.1. Topoi as Generalized Spaces -- 3.2. Local homeomorphisms, sheaves, and étale maps -- 3.3. The étale topology on ı-topoi |
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Chapter 4. Structured ı-Topoi -- 4.1. Structure Sheaves and Classifying Topoi -- 4.2. Geometries and Geometric Structures -- 4.3. Étale Morphisms of Structured ı-Topoi -- Chapter 5. Étendues: Gluing Local Models -- 5.1. Étendues -- 5.2. The functor of points approach -- 5.3. A classification of the functor of points. -- Chapter 6. Examples -- 6.1. Higher Differentiable Orbifolds and Étale Stacks -- 6.2. Deligne-Mumford Stacks for a Geometry -- Bibliography -- Back Cover |
| Summary |
The author develops a universal framework to study smooth higher orbifolds on the one hand and higher Deligne-Mumford stacks (as well as their derived and spectral variants) on the other, and use this framework to obtain a completely categorical description of which stacks arise as the functor of points of such objects. He chooses to model higher orbifolds and Deligne-Mumford stacks as infinity-topoi equipped with a structure sheaf, thus naturally generalizing the work of Lurie, but his approach applies not only to different settings of algebraic geometry such as classical algebraic geometry, |
| Notes |
"March 2020, volume 264, number 1282 (fifth of 6 numbers)." |
| Bibliography |
Includes bibliographical references |
| Subject |
Toposes.
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Categories (Mathematics)
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Orbifolds.
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Categorías (Matemáticas)
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Topos (Matemáticas)
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Categories (Mathematics)
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Orbifolds
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Toposes
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Category theory; homological algebra {For commutative rings see 13Dxx, for associative rings 16Exx, for groups 20Jxx, for topological groups and related structures 57Txx; see also 55Nxx and 55Uxx for.
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Algebraic geometry -- Families, fibrations -- Stacks and moduli problems.
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Global analysis, analysis on manifolds [See also 32Cxx, 32Fxx, 32Wxx, 46-XX, 47Hxx, 53Cxx] {For geometric integration theory, see 49Q15} -- General theory of differentiable manifolds [See also 32Cxx]
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| Form |
Electronic book
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| ISBN |
9781470458102 |
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1470458101 |
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