Higher orbifolds and deligne-mumford stacks as structured infinity-topoi / David Joseph Carchedi. [electronic resource]

By:

Carchedi, David Joseph [author.]

Material type: Text

TextSeries: Memoirs of the American Mathematical Society ; Volume 264, Number 1282.Publisher: Providence, RI : American Mathematical Society, 2020Description: 1 online resource (132 pages)Content type:

Media type:

Carrier type:

ISBN:

9781470458102 (e-book)

Subject(s):

Genre/Form:

Electronic books.

Additional physical formats: Print version:: Higher orbifolds and deligne-mumford stacks as structured infinity-topoi.DDC classification:

516/.07 23

LOC classification:

QA169 .C373 2020

Online resources:

Click to View

Summary: "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 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"-- Provided by publisher.

Holdings ( 1 )
Title notes ( 4 )

Holdings
Item type	Current library	Call number	Status	Date due	Barcode
Ebook	TUS: Midlands, Main Library Athlone Online	eBook (Browse shelf(Opens below))	Available

Includes bibliographical references.

"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 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"-- Provided by publisher.

Description based on print version record.

Electronic reproduction. Ann Arbor, MI : ProQuest, 2018. Available via World Wide Web. Access may be limited to ProQuest affiliated libraries.