# State of the art on a question on the existence of dualizing complex

Let A be a noetherian ring and D(A) be the derived category of modules on A. Recall that a dualizing complex for A is an object R in D(A) of finite injective dimension, with cohomology of finite type and such that the natural morphism of functors $Id \longrightarrow R\mathcal{H}om(R\mathcal{H}om(., R), R )$ is an isomorphism of functors.

In the book "Residues and Duality" (R. Hartshorne) (V.10), it is presented as an open problem to know if a noetherian local domain of dimension 1 admits a dualizing complex.

What is the state of the art on this question ?

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