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 ? 



State of the art on a question on the existence of dualizing complex
R.Y. Sharp proved in the 80s that a Noetherian ring with a dualizing complex must be "acceptable". This is a weakening of "excellent" obtained by replacing every occurence of the word "regular" with "Gorenstein", so means (1) universally catenary, (2) Gorenstein formal fibers, and (3) Gorenstein locus open in any finitely generated algebra. 


There is an example due to Ferrand and Raynaud of a one-dimensional noetherian domain for which the generic formal fiber is not Gorenstein. Such a ring does not, by Sharp's result, have a dualizing complex. 


