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Results tagged with gerbes
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user 11682
"Gerbe" is a construct in homological algebra and topology. They can be seen as a generalization of principal bundles to the setting of 2-categories. "Gerbe" is a French (and archaic English) word that literally means wheat sheaf. Gerbes were introduced by Jean Giraud (Giraud 1971) following ideas of Alexandre Grothendieck as a tool for non-commutative cohomology in degree 2.
4
votes
Phenomena of gerbes
A typical example from deformation theory : fix $i:X_0\to X$ of first order thickening defined by a square zero ideal $\mathcal I$, and let $\mathcal E_0$ be a locally free sheaf of finite rank on $X …
- 4,008
18
votes
Phenomena of gerbes
You can get a lot of examples by dimension shifting. Namely, consider any exact sequence of groups $$1\to K\to G \to H\to 1 \; .$$ Fix a $H$-torsor $T$. The stack $\mathcal G_T$ of liftings of the str …
- 4,008