  Let $R$ denote a Noetherian ring and an ideal $J \subset R$ with $U =
\operatorname{Spec R} \setminus V(J)$. For an $R$-module $M$ there is an
isomorphism $\Gamma(U, \tilde{M}) \cong \varinjlim \operatorname{Hom}_R(J^n,M)$
known as Deligne's formula (see [R. Hartshorne: Algebraic Geometry, Springer,
1983] and Deligne's Appendix in [R. Hartshorne: Residues and Duality, Lecture
Notes in Math. 20, Springer,1966] ). We extend the isomorphism for any
$R$-module $M$ in the non-Noetherian case of $R$ and $J = (x_1,\ldots,x_k)$ a
certain finitely generated ideal. Moreover, we recall a corresponding sheaf
construction.
