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gerbe
gerbe
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tangent complex
See formally smooth. Necessity of gerbes:
- stacks MOC
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classifying space
Computing the torsion classes of \(H^{*}(B \mathcal{G} ; \mathbb{Z})\) is an important problem; for example \(H^{3}(B \mathcal{G} ; \mathbb{Z})\) classifies the set of gerbes. # Unknown?
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Brauer group
More generally, \(H^2(X;{\mathbf{G}}_m)\) for \(X\in {\mathsf{Sch}}\) classifies gerbes over \(X\) with structure group \({\mathbf{G}}_m\).