.
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]
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.
Undergraduate Texts in Mathematics
Graduate Studies in Mathematics
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