# Tagged Questions

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votes

**1**answer

90 views

### The Existence of Pure Resolutions, Given a Degree Sequence?

I have been trying to understand the proof of the following theorem for the last month, I read some basics of sheaves theory and their cohomology, but still can't get the idea of this important ...

**1**

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**0**answers

194 views

### What is your expectation of the depth?

Let $S=k[x_1,...,x_9]$ be a polynomial ring over field $k$. Set $q_1=(x_1,x_2,x_5,x_6)$, $q_2=(x_1,x_2,x_6,x_7)$, $q_3=(x_2,x_3,x_7,x_8)$, $q_4=(x_1,x_5,x_6,x_7)$, $q_5=(x_1,x_6,x_7,x_8)$, ...

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**1**answer

153 views

### 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 ...

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**1**answer

140 views

### 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?

**2**

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**3**answers

362 views

### Computing the cardinality of cohomology groups

I hope this question is not unreasonably broad. It is about calculating or at least bounding the cardinality of cohomology groups in case they are finite.
Let us assume we are given a group $G$ and a ...

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**1**answer

142 views

### Artinian property of local cohomology module over graded local ring

We know that if $(R, m)$ is a local ring, $M$ is a finitely generated $R$-module, then the local cohomology module $H^{i}_{m}(M)$ is an Artinian module for every $j$.
My question is : if $(R,m)$ is a ...

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**2**answers

461 views

### vanishing of local cohomology $H^2_{(x,y)}\left(\frac{\Bbb Z[x,y]}{(5x+4y)}\right)=0$

Edited:
I guess
$$H^2_{(x,y)}\left(\frac{\Bbb Z[x,y]}{(5x+4y)}\right)=0$$
We know that if $\operatorname{Supp} H^i_I(M)\subseteq V(I)\cap \operatorname{Supp}(M)$, then
$$\operatorname{Supp} ...

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**1**answer

222 views

### Generalized Picard group (reflexive fractional ideals, principal ideals)

Given $\mathcal{O}=k[[u,v]]$ with maximal ideal $\mathfrak{m}$ and an $\mathcal{O}$-algebra $A$, free as an $\mathcal{O}$-module of rank $n^2$. $A$ is genertaed by two elements $x,y$ with $x^n=u$, ...

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**1**answer

231 views

### Cohomology of the general linear group on punctured spectra of 2-dim. power series rings

Let $(A,\mathfrak{m})=k[[x,y]]$ with $char(k)=0$ and $K=Quot(A)$. Set $X=Spec(A)$, $U=Spec(A)\backslash \lbrace \mathfrak{m} \rbrace$ the pointed spectrum. Furthermore given an $A$-algebra $B$, which ...

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**0**answers

347 views

### Cohomology and tensor product

Let $G$ be a profinite group, $A$ a free $\mathbb{Z}_p$-module of finite rank with a continuous action of $G$ and $B$ any $\mathbb{Z}_p$-module (I am not supposing it to be free), with the trivial ...

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**1**answer

216 views

### ideal transform

Let $I$ be an ideal of a commutative ring $R$. $M$ be an $R$-module. In Local cohomology: an algebraic introduction with geometric applications of Brodmann M. P., Sharp R. Y we have
$$D_I(M)=\mathop ...

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**1**answer

695 views

### Flat cohomology and Picard groups

Let $(R,m)$ be a local complete intersection of dimension $3$. Let $X=Spec(R)$ and $U=Spec(R) -\{m\}$ be the punctured spectrum of $R$. I am trying to understand the following comment by Gabber (see ...

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**1**answer

241 views

### Classifying Algebra Extensions over a fixed extension?

There are lots of "Ext groups" in homological algebra which measure extensions of various things. I'm sure there must be a homological algebra machine for computing the following, and I'm hoping that ...

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**2**answers

331 views

### What is the homology of the real coordinate ring of SO(n,R)? Other compact matrix groups?

As someone whose knowledge of cohomology is patchy and picked up on a need-to-know basis, and whose algebraic geometry is even worse, I wondered if someone could help with this question. (I ran into ...