I've been looking many places, but everything I find seems to either talk about (a) varieties or (b) extremely general situations with dualizing complexes. As I am not in the situation of (a) (i.e. over a field), and I don't yet understand (b), I was wondering if there was some place which talks about the middle ground. Specifically:

Let $X$ be a Noetherian, regular scheme of finite type over $\mathbb{Z}_p$, but not smooth. Then I've read in many places (even with just Cohen-Macaulay) that the dualizing complex is just a sheaf. Is there an "elementary" description of this sheaf?

Any references would be greatly appreciated.