Higher orbifolds and Deligne-Mumford stacks as structured infinity-topoi
Author(s)
Bibliographic Information
Higher orbifolds and Deligne-Mumford stacks as structured infinity-topoi
（Memoirs of the American Mathematical Society, no. 1282）
American Mathematical Society, c2020
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Note
"March 2020, volume 264, number 1282 (fifth of 6 numbers)"
Includes bibliographical reference (p. 119-120)
Description and Table of Contents
Description
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, derived algebraic geometry, and the algebraic geometry of commutative ring spectra 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 Deligne-Mumford stacks. This specializes to a new categorical description of classical Deligne-Mumford stacks, which extends to derived and spectral Deligne-Mumford stacks as well.
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