Tagged Questions

0
votes
0answers
6 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?
5
votes
1answer
122 views

Vanishing of local cohomology $\operatorname{H}^1_J(\Gamma_I(M))=0$

Let $M$ be a module over Noetherian ring $R$ such that $\operatorname{H}^1_I(M)=0$ for every ideal $I$ of $R$. Show that $\operatorname{H}^1_J(\Gamma_I(M))=0$ for every ideal $J$. I tried to prove it ...
3
votes
1answer
187 views

Vanishing of a local cohomology module

I guess $$H^2_{(x,y)}\left(\frac{\Bbb Z[x,y]}{(5x+4y)}\right)=0$$ It is well known $\operatorname{Supp} H^i_I(M)‎\subseteq V(I)\cap \operatorname{Supp}(M)$, therefore $$\operatorname{Supp} ...
1
vote
1answer
66 views

Comparing two different conditions for an ideal to correspond to a closed subscheme

Let $I$ be an ideal in the graded ring $S = A[x_0, \ldots, x_r]$. In Exercise II.5.10(a), Hartshorne defines the saturation $\bar I$ of $I$ to be the set $$\bar I = \{s \in S \mid \text{for all } i = ...