Krull dimension
Assuming formula_24 is a localization of a finite type formula_23-algebra, existence of a rigid dualizing complex over formula_24 relative to formula_23 was first proved by Yekutieli and Zhang assuming formula_23 is a regular noetherian ring of finite Krull dimension, and by Avramov, Iyengar and Lipman assuming formula_23 is a Gorenstein ring of finite Krull dimension and formula_24 is of finite flat dimension over formula_23.