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Author Carchedi, David Joseph, author.

Title Higher orbifolds and Deligne-Mumford stacks as structured infinity-topoi / David Joseph Carchedi
Published Providence, RI : American Mathematical Society, [2020]
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Description 1 online resource (v, 120 pages)
Series Memoirs of the American Mathematical Society ; number 1282
Memoirs of the American Mathematical Society ; no. 1282
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
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 Categories (Mathematics)
Orbifolds.
Toposes.
Algebraic geometry -- Families, fibrations -- Stacks and moduli problems.
Categories (Mathematics)
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.
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]
Orbifolds
Toposes
Form Electronic book
ISBN 1470458101
9781470458102