| 词条 | Regular scheme |
| 释义 |
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
References1. ^{{citation|title=Algebraic Geometry|volume=52|series=Graduate Texts in Mathematics|first=Robin|last=Hartshorne|authorlink=Robin Hartshorne|publisher=Springer|year=1977|isbn=9780387902449|page=238|url=https://books.google.com/books?id=3rtX9t-nnvwC&pg=PA238}}. {{algebraic-geometry-stub}}2. ^{{citation|title=Introduction to algebraic geometry and algebraic groups|volume=39|series=North-Holland Mathematics Studies|publisher=North-Holland|first=Michel|last=Demazure|authorlink=Michel Demazure|year=1980|isbn=9780080871509|at=Proposition 3.2, p. 168|url=https://books.google.com/books?id=RDKRyP00aoMC&pg=PA168}}. 2 : Algebraic geometry|Scheme theory |
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