A note on Deligne's formula

Abstract

Let R denote a Noetherian ring and an ideal J ⊂ R with U = Spec R \ V (J). For an R-module M there is an isomorphism Γ(U, ˜M ) ∼= 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-Noetherian case of R and J = (x1, . . . , xk ) a certain finitely generated ideal. Moreover, we recall a corresponding sheaf construction.