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Results tagged with stacks
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user 24965
In mathematics a stack or 2-sheaf is a sheaf that takes values in categories rather than sets.
3
votes
1
answer
232
views
Is the cotangent complexes of groupoids bounded above by degree $1$?
Let $\mathcal{X}$ be a stack given by a groupoid $X_1\rightrightarrows X_0$, where $X_0$ and $X_1$ are smooth $k$-varieties. Let $\mathbb{L}_{\mathcal{X}/k}$ be the cotangent complex of $\mathcal{X}$ …
- 9,019
10
votes
0
answers
204
views
Does the category of $G$-equivariant sheaves have enough injectives?
I am not sure if this question is the same as the existence of enough injectives in the category of sheaves on stacks. …
- 9,019
6
votes
0
answers
169
views
How to realize the descent data of Qcoh as a (pseudo)-limit in Cat?
It is well-know that $Qcoh$ is a fibered category on $Sch$. In more details let $\mathcal{C}$ be the category $(Sch/S)$ of schemes over a fixed base scheme S. For each scheme $U$ we define $Qcoh(U)$ …
- 9,019
1
vote
0
answers
191
views
Why $D^b(S)\cong D^b_{\text{Car}}(\text{cosq}(X\rightarrow S))$?
Let $p: X\rightarrow S$ be a map between topological spaces and we can construct the simplicial space $\text{cosq}(X\rightarrow S)$ where $X_0=X$, $X_1=X\times_S X$ and
$$
X_n=\underbrace{ X\times_S \ …
- 9,019