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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

√Čtale morphism
Dimension of an algebraic variety
Glossary of scheme theory
Smooth completion


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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