I'm looking for spectral sequences to involve together two ideals of a ring. For instance, let $I,J$ be two ideals of Noetherian ring $R$ and $M$ be a finite $R$-module then we have the following spectral sequences $$H_I^i(H^j_J(M))‎\Rightarrow‎ H^{i+j}_{I+J}(M).$$ $$\operatorname{Ext}^i_R(R/I,H^j_J(M))\Rightarrow‎ \operatorname{Ext}^{i+j}_R(R/I,M),\quad \text{if}~~ J\subset I.$$

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    $\begingroup$ What is the purpose of this question? $\endgroup$ – Mariano Suárez-Álvarez Dec 28 '13 at 20:03
  • $\begingroup$ I wanna find a relation between $grade(I,M)$ and $grade(J,M)$. $\endgroup$ – Stella Dec 29 '13 at 9:43
  • $\begingroup$ Why don't you say so in the question? If you eexplain what you want, the chances of gettng what you want are immensely larger! $\endgroup$ – Mariano Suárez-Álvarez Dec 29 '13 at 17:22
  • $\begingroup$ @ann: Can you formulate your question in a bit more detail? For instance, let $(R,m)$ be a local (or Cohen-Macaulay) ring, $I = m$, and $M = R$. Then what you are looking for is just grade $J$ which is arbitrary in general. It would be interesting if one can come up with a formula. $\endgroup$ – Youngsu Dec 29 '13 at 20:34

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