Let $R$ be a reduced Noetherian ring. Assume $R$ is quasi-excellent and Cohen-Macaulay.



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> Is $R$ the quotient of a Gorenstein ring?
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If the answer is yes, then $R$ has a dualizing complex. The question can, therefore, be rephrased into:
"is there an example of a reduced quasi-excellent Cohen-Macaulay ring that does not admit a dualizing complex?"



Quotients of Gorenstein rings
No, $R$ is not necessarily a quotient of a Gorenstein ring, because of the following:


**Example** [[Nishimura 2012](https://doi.org/10.1215/21562261-1503754), Example 6.1]**.** *There exists a two-dimensional Cohen–Macaulay factorial excellent local domain with a Gorenstein module, which has no dualizing (i.e., canonical) module.*


Nishimura attributes the construction to [[Weston 1988](https://doi.org/10.1016/0021-8693(88)90021-X)] and [[Ogoma 1982](https://mathscinet.ams.org/mathscinet-getitem?mr=643928), Section 4].


