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Record Nr. |
UNINA9910478858503321 |
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Autore |
Carchedi David Joseph |
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Titolo |
Higher orbifolds and deligne-mumford stacks as structured infinity-topoi / / David Joseph Carchedi |
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Pubbl/distr/stampa |
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Providence, RI : , : American Mathematical Society, , 2020 |
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ISBN |
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Descrizione fisica |
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1 online resource (132 pages) |
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Collana |
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Memoirs of the American Mathematical Society, , 0065-9266 ; ; Volume 264, Number 1282 |
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Disciplina |
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Soggetti |
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Algebraic geometry -- Families, fibrations -- Stacks and moduli problems |
Toposes |
Orbifolds |
Categories (Mathematics) |
Electronic books. |
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Lingua di pubblicazione |
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Formato |
Materiale a stampa |
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Livello bibliografico |
Monografia |
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Nota di bibliografia |
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Includes bibliographical references. |
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Sommario/riassunto |
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"We develop 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. We choose to model higher orbifolds and Deligne-Mumford stacks as infinity-topoi equipped with a structure sheaf, thus naturally generalizing the work of Lurie (2004), but our approach applies not only to different settings of algebraic geometry such as classical algebraic geometry, derived algebraic geometry, and the algebraic geometry of commutative ring spectra as in Lurie (2004), but also to differential topology, complex geometry, the theory of supermanifolds, derived manifolds etc., where it produces a theory of higher generalized orbifolds appropriate for these settings. This universal framework yields new insights into the general theory of Deligne-Mumford stacks and orbifolds, including a representability criterion which gives a categorical characterization of such generalized |
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Deligne-Mumford stacks. This specializes to a new categorical description of classical Deligne-Mumford stacks, a result sketched in Carchedi (2019), which extends to derived and spectral Deligne-Mumford stacks as well"-- |
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