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