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


  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.

This article is issued from Wikipedia. The text is licensed under Creative Commons - Attribution - Sharealike. Additional terms may apply for the media files.