Holmstrom Morphism of schemes

Maybe make a table with overview. Possible sources: FGA book.


Many notions, such as smooth, flat, etale, proper, open immersion, can be defined in the much more general contexts of Toen. See for example HAG II, the Barcelona notes, and the Brave new algebraic geometry paper.

http://mathoverflow.net/questions/15474/functorial-characterization-of-morphisms-of-schemes


From review of Murre lectures on fundamental gp: A flat morphism is open. A faithfully flat morphism is an effective epimorphism.


For reference, we collect here some basic definitions of various kinds of morphisms of schemes.

Projective

Smooth

Quasi-projective

Finite type

Open

Proper

Separated

Local complete intersection

“E.g. any morphism between smooth k-schemes”

nLab page on Morphism of schemes

Created on June 9, 2014 at 21:16:13 by Andreas Holmström