All Questions
Tagged with algebraic-stacks dg.differential-geometry
7 questions
0
votes
0
answers
144
views
Cartesian square in the category of Algebraic stacks
Suppose we have a commutative diagram of Artin stacks
$ \newcommand{\ra}[1]{\kern-1.5ex\xrightarrow{\ \ #1\ \ }\phantom{}\kern-1.5ex} \newcommand{\ras}[1]{\kern-1.5ex\xrightarrow{\ \ \smash{#1}\ \ }\...
- 494
1
vote
0
answers
125
views
2-shifted 2-form on the classifying stack 𝐵𝐺
Let $G$ be a reductive group. A $2$-shifted $2$-form on the classifying stack $BG$ is by definition a a morphism of quasi-coherent complexes
\begin{equation}
\mathcal O_{BG}\rightarrow (\wedge^2 \...
- 494
1
vote
0
answers
309
views
Is there an intrinsic Gauss map?
$\DeclareMathOperator\GL{GL}\DeclareMathOperator\Gr{Gr}$This may all be well known, too vague, or stupid; my apologies.
The Gauss map is defined by embedding your $k$-dimensional smooth scheme/...
- 1,084
20
votes
7
answers
3k
views
What are the occurrences of stacks outside algebraic geometry, differential geometry, and general topology?
What are the occurrences of the notion of a stack outside algebraic geometry, differential geometry, and general topology?
In most of the references, the introduction of the notion of a stack takes ...
- 6,023
4
votes
0
answers
278
views
connection on principal bundles over algebraic/geometric stacks
Is there a notion of connection on a principal bundle over an algebraic or geometric stack?
By a geometric stack, I mean a stack over category of manifolds that is representable by a Lie groupoid; ...
- 6,023
5
votes
1
answer
366
views
K-theory for a (geometric) stack
There is a notion of $K$-theory for a manifold $M$.
Is there a notion of $K$-theory for a stack $\mathcal{D}\rightarrow \text{Man}$ that is representable by a Lie groupoid $\mathcal{G}$; that is $...
- 6,023
2
votes
0
answers
348
views
Notions of algebraic/differential geometry of scheme/manifolds extended to algebraic/differential stacks
Given a manifold, one can associate a stack over the category of manifolds, which is a differential geometric stack. This gives a functor $\text{Man}\rightarrow \text{D.Stacks}$. This is an embedding....
- 6,023