All Questions
Tagged with local-cohomology cohomology
7 questions
0
votes
1
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201
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Are these two natural cohomology classes of a manifold constructed from a 1-cochain and a group extension equal?
Let $X$ be a manifold, $G$ and $A$ finite abelian groups and $\epsilon \in H^2(G,A)$ a group cohomology class (for the moment I am assuming there is no action of $G$ on $A$). Given $\alpha \in H^1(X,G)...
- 813
1
vote
0
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57
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Sequence in local cohomology for multiple closed subsets
Let $X$ be topological space with closed subsets $A,B,C \subset X$ and $\mathcal{F} \in Sh(X)$.
I'm trying to understand
\begin{equation*}
H^i_{A\cap B}(X,\mathcal{F}) \oplus H^i_{A\cap C}(X,\mathcal{...
- 473
3
votes
0
answers
197
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Comparing long exact sequences for local cohomology
Let $X$ be a topological space, $Z_1,Z_2 \subset X$ closed subsets and $\mathcal{F} \in Sh(X)$.
Then we have, for example by Hartshorne Excercise III 2.4, the Mayer Vietoris sequence for local ...
- 473
5
votes
1
answer
615
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Difference between local cohomology and cohomology with support in a family
Let $X$ be a topological space. A collection of closed subsets of $X$ is called a family of supports (in the sense of Cartan) if: (1) the union of any two elements of $\Phi$ is an element of $\Phi$, ...
- 3,101
1
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0
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296
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What is your expectation of the depth?
Let $S=k[x_1,...,x_9]$ be a polynomial ring over field $k$. Set $q_1=(x_1,x_2,x_5,x_6)$, $q_2=(x_1,x_2,x_6,x_7)$, $q_3=(x_2,x_3,x_7,x_8)$, $q_4=(x_1,x_5,x_6,x_7)$, $q_5=(x_1,x_6,x_7,x_8)$, $q_6=(x_2,...
- 21
1
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1
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211
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Is there a prime of height $i$ in support of $H^i_I(R)$?
$I$ is an ideal of a local Noetherian ring $R$ and $i>0$ .
Clearly the height of primes in support of $H^i_I(R)$ is at least $i$
The question is if it
contains a prime of height $i$, specially ...
- 189
1
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1
answer
234
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Relation between $H^i_I(-)$ and $H^i_J(-)$ when $I\subset J$
What is the relation between $H^i_I(-)$ and $H^i_J(-)$ (cohomological functors) when $I\subset J$ are ideals of a (local) noetherian ring?
- 189