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101 0 $aeng
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181   $ctxt$2rdacontent
182   $cc$2rdamedia
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200 10$aHigher orbifolds and deligne-mumford stacks as structured infinity-topoi /$fDavid Joseph Carchedi
210  1$aProvidence, RI :$cAmerican Mathematical Society,$d2020.
215   $a1 online resource (132 pages)
225 1 $aMemoirs of the American Mathematical Society,$x0065-9266 ;$vVolume 264, Number 1282
311   $a1-4704-4144-6 
320   $aIncludes bibliographical references.
330   $a"We develop a universal framework to study smooth higher orbifolds on the one hand and higher Deligne-Mumford stacks (as well as their derived and spectral variants) on the other, and use this framework to obtain a completely categorical description of which stacks arise as the functor of points of such objects. We choose to model higher orbifolds and Deligne-Mumford stacks as infinity-topoi equipped with a structure sheaf, thus naturally generalizing the work of Lurie (2004), but our approach applies not only to different settings of algebraic geometry such as classical algebraic geometry, derived algebraic geometry, and the algebraic geometry of commutative ring spectra as in Lurie (2004), but also to differential topology, complex geometry, the theory of supermanifolds, derived manifolds etc., where it produces a theory of higher generalized orbifolds appropriate for these settings. This universal framework yields new insights into the general theory of Deligne-Mumford stacks and orbifolds, including a representability criterion which gives a categorical characterization of such generalized Deligne-Mumford stacks. This specializes to a new categorical description of classical Deligne-Mumford stacks, a result sketched in Carchedi (2019), which extends to derived and spectral Deligne-Mumford stacks as well"--$cProvided by publisher.
410  0$aMemoirs of the American Mathematical Society ;$vVolume 264, Number 1282.
606   $aAlgebraic geometry -- Families, fibrations -- Stacks and moduli problems$2msc
606   $aToposes
606   $aOrbifolds
606   $aCategories (Mathematics)
615  7$aAlgebraic geometry -- Families, fibrations -- Stacks and moduli problems.
615  0$aToposes.
615  0$aOrbifolds.
615  0$aCategories (Mathematics)
676   $a516/.07
686   $a18B25$a14D23$a58A03$2msc
700   $aCarchedi$b David Joseph$01715713
801  0$bMiAaPQ
801  1$bMiAaPQ
801  2$bMiAaPQ
906   $aBOOK
912   $a9910820874903321
996   $aHigher orbifolds and deligne-mumford stacks as structured infinity-topoi$94110585
997   $aUNINA