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Results tagged with gerbes
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user 4149
"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.
1
vote
Accepted
gluing gerbes over a spectrum of a field
I don't think so. I think a gerbe bound by $A$ over the spectrum of a field $k$ gives a cohomology class $\eta\in H^2(k,A)$, and the gerbe trivializes over an extension $k'/k$ if and only if this c …
- 14.2k
2
votes
2
answers
381
views
Constructing a stack (gerbe) from a connected groupoid
Let $\mathcal{G}=(A\rightrightarrows X)$ be a groupoid.
Here $X={\rm Ob}(\mathcal{G})$, $A={\rm Ar}(\mathcal{G})$,
and we have 5 maps:
$s,t\colon A\to X$ (the source and the target, surjective),
$m\co …
- 14.2k
5
votes
Second nonabelian group cohomology: cocycles vs. gerbes
Nonabelian $H^2$ in Galois cohomology can be defined in terms of: (1) cocycles, (2) extensions, (3) gerbes. …
- 14.2k
19
votes
3
answers
2k
views
Second nonabelian group cohomology: cocycles vs. gerbes
Giraud in his book (page 452) writes that "la définition de $H^2$ en termes de gerbes ... redonne, dans ce cas, la théorie de Springer".
I do not understand the latter assertion. … Giraud defines $H^2$ in terms of gerbes (on the category of $\Gamma$-sets?).
Question: How can I get a gerbe $\mathcal{G}$ (i.e., a stack over the category of $\Gamma$-sets) from a group extension? …
- 14.2k