Smooth scheme

In algebraic geometry, a smooth scheme X of dimension n over an algebraically closed field k is an algebraic scheme that is regular and has dimension n. More generally, an algebraic scheme over a field k is said to be smooth if is smooth for any algebraic closure of k. If k is perfect, then an algebraic scheme over k is smooth if and only if it is regular. There is also a notion of a “smooth morphism” between schemes, and the above definition coincides with it.