All Questions
Tagged with derived-categories cohomology
10 questions with no upvoted or accepted answers
9
votes
0
answers
311
views
Evens norm as a derived functor
In the theory of cohomology of groups there are several important maps between cohomologies: restriction, inflation, transfer and Evens norm. The first three of them can be clearly seen on the level ...
- 1,484
5
votes
0
answers
321
views
Appropriate notion of derived category over condensed set
If we have a compact Hausdorff space $S$, then my understanding is that the appropriate notion of the derived category of sheaves of condensed abelian groups is to consider the derived category $D_{\...
- 163
5
votes
0
answers
160
views
Extension groups in quotient categories
Let $\mathcal{A}$ be an abelian category and let $\mathcal{B}$ be a Serre subcategory of $\mathcal{A}$. We can form the quotient category $\mathcal{A}/\mathcal{B}$, and the canonical functor $Q:\...
- 1,479
4
votes
0
answers
202
views
Cohomological methods in intersection theory and derived categories
Are there any enumerative questions akin to: “What is the number of planes containing a given line tangent to a given cubic surface in $\mathbb{P}^3$” that we can answer using derived categories? I've ...
- 511
4
votes
0
answers
173
views
Reference for equivariant derived Künneth formula
I'm looking for a reference for the following statement in as much generality as possible, assuming it is correct.
Let's $X$ and $Y$ be "spaces" with a $G$-action. We can take the $G$-product defined ...
- 41
3
votes
0
answers
213
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2 K3s and cubic fourfolds containing a plane
Two K3 surfaces show up when talking about cubic fourfolds containing a plane. Let $P\subset X\subset \mathbb{P}^5$ be the plane inside the cubic. Since $P$ is cut out by 3 linear equations then $X$ ...
- 3,779
3
votes
0
answers
424
views
Stalks of perverse cohomology sheaves?
For a complex of sheaves $\cal{F}^{\bullet}$ on a variety $X$, a useful fact is that the stalks of the cohomology sheaves of $\mathcal{F}^{\bullet}$ agree with the cohomology groups of the complex of ...
- 1,701
2
votes
0
answers
214
views
Hochschild cohomology of a sheaf of associative algebras
Assume that $X$ is a complex manifold. Let $\delta: X\to X\times X$ be the diagonal map. Assume that $\mathcal{A}_X$ is a $\mathbb C_X$-algebra and $\mathcal{M}_X$ is a left $\mathcal{A}_X\otimes_{\...
- 609
2
votes
0
answers
76
views
Cohomology of sheaves on $X \cup_{Z} Y$
I am in the following situation, I have two schemes $X$, $Y$ and two closed immersions $Z \rightarrow Y$, $Z \rightarrow X$. Everything is smooth. I am interested in calculating morphisms in the ...
- 1,325
0
votes
0
answers
95
views
$\operatorname{Ext}$-group in the category of modules versus in the subcategory of finitely generated ones
I am trying to refine my understanding of derived categories.
Let $\text{Mod}_R$ and $\text{Mod}^f_R$ be respectively the categories of modules and finitely generated modules over a Notherian ring $R$ ...
- 1,479