In algebraic geometry, a regular scheme is a locally Noetherian scheme whose local rings are regular everywhere. [1] [2] Every smooth scheme is regular, and every regular scheme of finite type over a perfect field is smooth. [3]
For an example of a regular scheme that is not smooth, see Geometrically regular ring#Examples.
In algebraic geometry, a regular scheme is a locally Noetherian scheme whose local rings are regular everywhere. [1] [2] Every smooth scheme is regular, and every regular scheme of finite type over a perfect field is smooth. [3]
For an example of a regular scheme that is not smooth, see Geometrically regular ring#Examples.