The gerbes tag has no usage guidance.

**9**

votes

**0**answers

300 views

### Geometrizing the Third Cohomology of a Complex Lie Group

If $G_\mathbb{C}$ is a simply-connected simple complex Lie group, theorem 5.4.10 of Brylinski's "Loop Spaces, Characteristic Classes, and Geometric Quantization" claims that there is a natural ...

**8**

votes

**0**answers

268 views

### Are deformations of a scheme some kind of a “derived gerbe” under the cotangent complex?

(This is probably a very naive question. My understanding of the cotangent complex is quite vague.)
Let me first recall the picture for deformations of a smooth morphism:
If $f:X_0\to S_0$ is a ...

**4**

votes

**0**answers

246 views

### Differential Geometry of (Non-Abelian) Gerbes in the language of Brylinski

Context
In an effort to have a definition for connection on a non-abelian gerbe, in the style of Brylinski, I am reading Breen and Messing's Differential Geometry of Gerbes [BM]. It seems that there ...

**4**

votes

**0**answers

660 views

### 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 ...

**3**

votes

**0**answers

117 views

### Writing down gerbes explicitly over the projective line

Let $X = [\mathbb P^1/(\mathbb Z/2\mathbb Z)]$, where we take the trivial action of $\mathbb Z/2\mathbb Z$ on $\mathbb P^1$. Is this DM stack over $\mathbb C$ a gerbe over $\mathbb P^1$? Is it the ...

**2**

votes

**0**answers

37 views

### Connection on 3-bundle given as triplet of forms

A connection on a bundle is given locally by a Lie algebra-valued 1-form.
Gauge transformations act in the usual way on the forms, and form a groupoid.
A connection on a 2-bundle is given locally by ...

**2**

votes

**0**answers

232 views

### A Fourier-Mukai type duality for gerbes, torsors and their duals

Here is a result whose proof uses Fourier-Mukai duality:
Consider a family of abelian varieties $A \rightarrow X$, its dual $\check{A} \rightarrow X$, and a torsor $\mathcal{T}$ (for $A \rightarrow ...

**1**

vote

**0**answers

175 views

### Mayer-Vietoris on Fibered Products

Suppose $M \xrightarrow{p} X$ is a surjective submersion of smooth manifolds. Define the fibered product in this case: $$M \times_X M = \{ (m_1, m_2) \in M \times M | p(m_1) = p(m_2) \}$$
and let $U ...

**1**

vote

**0**answers

118 views

### The Abelian Group of Equivalence Classes of Gerbes

Are there any good references/explanations for understanding the "contracted product" (as Brylinski calls it) of a gerbe with abelian band? I am finding it difficult, using Brylisnki's definition. to ...

**0**

votes

**0**answers

127 views

### Where are there defined objects between gerbes and bundle gerbes?

Consider a special kind of/something like a gerbe where there is first given local trivialization data with equivalence over 2-fold overlaps but not isomorphism.
Does this exist in the literature?