Lemma 47.16.9. Let (A, \mathfrak m, \kappa ) be a Noetherian local ring with normalized dualizing complex. Let I \subset \mathfrak m be an ideal of finite length. Set B = A/I. Then there is a distinguished triangle
\omega _ B^\bullet \to \omega _ A^\bullet \to \mathop{\mathrm{Hom}}\nolimits _ A(I, E)[0] \to \omega _ B^\bullet [1]
in D(A) where E is an injective hull of \kappa and \omega _ B^\bullet is a normalized dualizing complex for B.
Comments (0)