Bitorseurs et Cohomologie Non Abélienne

Breen, Lawrence

doi:10.1007/978-0-8176-4574-8_10

Cited by 73 publications

(174 citation statements)

References 29 publications

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“…In this section we briefly recall the definition of cohomology with values in a stack and show how to describe it explicitly by means of crossed modules. References are made to [6,7] 7 . We assume that the reader is familiar with the notions of monoidal category, monoidal functor and monoidal transformation, and also with their stack counterpart.…”

Section: §4 Cohomology With Values In a Stackmentioning

confidence: 99%

Classiﬁcation of Deformation Quantization Algebroids on Complex Symplectic Manifolds

Polesello¹

2008

Publ. Res. Inst. Math. Sci.

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Section: §4 Cohomology With Values In a Stackmentioning

confidence: 99%

Classiﬁcation of Deformation Quantization Algebroids on Complex Symplectic Manifolds

Polesello¹

2008

Publ. Res. Inst. Math. Sci.

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“…We would like to thank Ettore Aldrovandi, Lev Borisov, Jean-Louis Colliot-Thélène, Andrew Kresch, Fabio Perroni, Ilya Tyomkin and Angelo Vistoli for helpful discussions; in particular Aldrovandi for explanations about group-stacks and reference [Bre90], Borisov for pointing out a mistake in a preliminary version, ColliotThélène for [Gro68,§6], Tyomkin for [BB93] and Vistoli for useful information about the classification of gerbes.…”

Section: Introductionmentioning

confidence: 99%

Smooth toric Deligne-Mumford stacks

Fantechi

Mann

Nironi

2010

Journal Für Die Reine Und Angewandte Mathematik (Crelles Journal)

132

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Abstract. We give a geometric definition of smooth toric Deligne-Mumford stacks using the action of a"torus". We show that our definition is equivalent to the one of Borisov, Chen and Smith in terms of stacky fans. In particular, we give a geometric interpretation of the combinatorial data contained in a stacky fan. We also give a bottom up classification in terms of simplicial toric varieties and fiber products of root stacks.

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“…For any topos T, and groups G, A in the topos with A abelian, there is a category whose objects are central extensions A ֒→ E ։ G of groups in T. Such extensions may be viewed as multiplicative A G -torsors, as in Breen [Bre90]. We write CExt(G, A) for the category of central extensions of G by A.…”

Section: Preliminariesmentioning

confidence: 99%

Covering groups and their integral models

Weissman

2015

Trans. Amer. Math. Soc.

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Abstract. Given a reductive group G over a base scheme S, Brylinski and Deligne studied the central extensions of a reductive group G by K 2 , viewing both as sheaves of groups on the big Zariski site over S. Their work classified these extensions by three invariants, for S the spectrum of a field. We expand upon their work to study "integral models" of such central extensions, obtaining similar results for S the spectrum of a sufficiently nice ring, e.g., a DVR with finite residue field or a DVR containing a field. Milder results are obtained for S the spectrum of a Dedekind domain, often conditional on Gersten's conjecture.

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Bitorseurs et Cohomologie Non Abélienne

Cited by 73 publications

References 29 publications

Classiﬁcation of Deformation Quantization Algebroids on Complex Symplectic Manifolds

Classiﬁcation of Deformation Quantization Algebroids on Complex Symplectic Manifolds

Smooth toric Deligne-Mumford stacks

Covering groups and their integral models

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