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
$$D\_I(M)=\mathop {\lim }\limits\_{\begin{subarray}{c} 
 \longrightarrow \\ 
\end{subarray}} Hom\_R(I^{n},M) $$
called ideal transform of $M$ respect to $I$ or $I-transform$ of $M$.
I heard someone talked about Deligne's formula but i can not find it. 
Can anyone help me to find it?
I think that, it is
$$D\_I(M)=\mathop {\lim }\limits\_{\begin{subarray}{c} 
 \longrightarrow \\ 
\end{subarray}} M\_a $$
where $M\_a$ is the localization of $M$ with respect to multiplicative systems of powers of a single $M$-regular element $a$ in $I$.



ideal transform
I've seen the following called Deligne's formula (it is in Hartshorne, Algebraic Geometry, Chapter III, Exercise 3.7), and I think essentially answers your question.


It says that if $Z = V(I)$ (the closed subset of $X = \text{Spec} R$) and $U = X \setminus Z$, then 
$$
\Gamma(U, \widetilde{M}) = \lim\_{\to} \text{ Hom}\_R(I^n, M)
$$


