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Results tagged with algebraic-stacks
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user 118688
20
votes
7
answers
3k
views
What are the occurrences of stacks outside algebraic geometry, differential geometry, and ge...
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
0
votes
A presentation of an algebraic stack is epi. in etale topology
A "similar" result along with proof can be found as Lemma 2.14 of Differentiable Stacks and Gerbes.
I would like to give more details if you want.
- 6,023
1
vote
Representaility of morphism of stacks for schemes
This is not an answer, just too long for a comment. So, writing as an answer. It turns out that, one may not be able to see the correspondence between these three definitions as one of them is stated …
- 6,023
5
votes
1
answer
362
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
1
answer
540
views
Stack associated to Groupoid object in category $\text{Sch}/S$
Consider the category of manifolds $\text{Man}$.
A groupoid object in the category of manifolds is called a Lie groupoid, denoted by $\mathcal{G}$. There is a way to associate a stack (over the cate …
- 6,023
4
votes
0
answers
1k
views
English translation of G.Laumon, L.Moret-Bailly book Champs algébriques
Is there an English translation of G.Laumon, L.Moret-Bailly book Champs algébriques.
Most questions on this site on stacks received this book as reference in comments/answers.
So, I want to ask if …
- 6,023
4
votes
0
answers
271
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; t …
- 6,023
3
votes
0
answers
460
views
Prerequisites for understanding algebraic geometry of “algebraic gerbes”
I am trying to learn about algebraic geometry of gerbes.
I am familiar with set up of gerbes in the case of differential geometry. Though there is some similarity between differentiable gerbes and ge …
- 6,023
2
votes
0
answers
340
views
Notions of algebraic/differential geometry of scheme/manifolds extended to algebraic/differe...
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
4
votes
0
answers
286
views
MSRI Workshop videos and lecture notes
I am referring to MSRI workshop "Introductory Workshop on Algebraic Stacks, Intersection Theory, and Non-Abelian Hodge Theory".
There are videos and lecture notes available which can be seen on click …
- 6,023
4
votes
1
answer
551
views
Stack being represented by a scheme/manifold
On page $10$ of the survey article Algebraic stacks, by T. Gomez (arXiv:math/9911199), we have following result
If a stack has an object with an automorphism other than the identity, then the sta …
- 6,023