A note on Deligne's formula

Let R denote a Noetherian ring and an ideal J subset of R with U = Spec R \ V (J). For an R-module M there is an isomorphism Gamma(U, M) similar to= lim ---> HomR(Jn, M) known as Deligne's formula (see [8, p. 217] and Deligne's Appendix in [7]). We extend the isomorphism for any R-module M in the non-No etherian case of R and J = (x1, ..., xk) a certain finitely generated ideal. Moreover, we recall a corresponding sheaf construction. (c) 2024 The Author. Published by Elsevier B.V. This is an open access article under the CC BY license (http://creativecommons .org /licenses /by /4 .0/).