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Regular scheme

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Not to be confused with regular embedding.

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

References

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


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