# Tagged Questions

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### Gerbes on the multiplicative group

Let $k$ be an arbitrary field with absolute Galois group $\Gamma$. The group $\text{Hom}(\Gamma,\mathbb{Q}/\mathbb{Z})$ injects into $H^2(\mathbb{A}^1 \setminus \{ 0 \},\mathbb{G}_m)$, as one can see ...
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### Recovering classical Tannaka duality from Lurie's version for geometric stacks

In Lurie's paper Tannaka Duality for Geometric Stacks, it is essentially shown that specifying a morphism of geometric objects $$f \colon X \to Y$$ is equivalent to giving a corresponding pullback ...
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### Is the first differential Pontryagin class a morphism of stacks?

In Cech Cocycles for Characteristic Classes, Jean-Luc Brylinski and Dennis McLaughlin provide explicit formulas for Cech cocycles for characteristic classes of real and complex vector bundles, and ...
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### Are bundle gerbes bundles of algebras?

The category of line bundles (possibly with connection) on a smooth manifold M can be defined in two different ways: The first definition uses transition functions that satisfy a cocycle condition (...
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### Bundle Gerbes as Characteristic Classes

Perhaps this is a bit naïve, but I was wondering if it possible to (at least formally) represent Bundle Gerbes as Characteristic Classes. Disclaimer: My understanding of Bundle Gerbes is limited to ...
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### What's a good reference about gerbes and bands?

I've seen several papers that I would like to read that use the language of gerbes and bands. The wiki page on gerbes is useful, but doesn't even contain the word 'band', so I'm left confused even ...
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### Why do gerbes live in H^2 ?

Line bundles on a scheme $X$ live in $H^1(X,O_X^*)$, where $O_{X}^{*}$ is the sheaf of invertible functions. If $X$ is noetherian separated, then we can think of this $H^1$ to be Cech cohmology w.r.t....
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### Algebraic versus Analytic Brauer Group

Let $X$ be a smooth projective algebraic variety over $\mathbb{C}$. Then I think that someone (Serre?) showed that the Cohomological Etale Brauer Group agrees with the torsion part of the Analytic ...