separated scheme
A scheme is defined to be a separated scheme if the morphism
into the fibre product which is induced by the identity maps in each coordinate is a closed immersion.
Note the similarity to the definition of a Hausdorff topological space. In the situation of topological spaces, a space is Hausdorff if and only if the diagonal morphism is a closed embedding of topological spaces. The definition of a separated scheme is very similar, except that the topological product is replaced with the scheme fibre product.
More generally, if is a scheme over a base scheme , the scheme is defined to be separated over if the diagonal embedding
is a closed immersion.
Title | separated scheme |
---|---|
Canonical name | SeparatedScheme |
Date of creation | 2013-03-22 12:50:25 |
Last modified on | 2013-03-22 12:50:25 |
Owner | djao (24) |
Last modified by | djao (24) |
Numerical id | 6 |
Author | djao (24) |
Entry type | Definition |
Classification | msc 14A15 |
Defines | separated |