Geometrically (algebraic geometry)

In algebraic geometry, especially in scheme theory, a property is said to hold geometrically over a field if it also holds over the algebraic closure of the field. In other words, a property holds geometrically if it holds after a base change to a geometric point. For example, a smooth variety is a variety that is geometrically regular.
Geometrically irreducible and geometrically reduced.
Given a scheme "X" that is of finite type over a field "k", the following are equivalent:
The same statement also holds if "irreducible" is replaced with "reduced" and the separable closure is replaced by the perfect closure.