Serre's condition 
for a Noetherian ring 
requires
 |
at every prime ideal 
. Here depth is the maximum length of a regular sequence in
the maximal ideal of the local
ring. A locally Noetherian scheme satisfies 
when its local rings do. The depth condition limits embedded
and low-codimension defects (Stacks Project n.d.).
It is required in the definition of a semi-log
canonical pair, alongside conditions on codimension-one
singularities.
