Regular scheme

In algebraic geometry, a regular scheme is a scheme whose local rings are regular everywhere.[1] Every smooth scheme is regular, and every regular scheme of finite type over a perfect field is smooth.[2]

For an example of a regular scheme that is not smooth, see Geometrically regular ring#Examples.

See also

• Étale morphism
• Dimension of an algebraic variety
• Glossary of scheme theory
• Smooth completion

References

1. Hartshorne, Robin (1977), Algebraic Geometry, Graduate Texts in Mathematics, 52, Springer, p. 238, ISBN 9780387902449.
2. Demazure, Michel (1980), Introduction to algebraic geometry and algebraic groups, North-Holland Mathematics Studies, 39, North-Holland, Proposition 3.2, p. 168, ISBN 9780080871509.