nLab relative dimension


For morphisms of schemes


Let f:XYf : X \to Y be a morphism locally of finite type between two schemes XX and YY. The relative dimension of ff at a point yYy \in Y is the dimension of the fiber f 1(y)f^{-1}(y). If all the nonempty fibers f 1(y)f^{-1}(y) (yYy \in Y) are purely? of the same dimension nn, then one says that ff is of relative dimension nn.


Though the definition does not seem to appear in EGA, there are some relevant propositions in (EGA, IV_2, 5.6):

Last revised on March 23, 2013 at 16:59:54. See the history of this page for a list of all contributions to it.