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Results tagged with flatness
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user 3521
7
votes
properties of the fibers of a flat morphism
Hi, here are some references taken from Algebraic geometry I. Schemes. by Gortz and Wedhorn, Appendix E. These are generally scattered in EGAIV as far as I remember. Anyway, Kazuma Shimomoto recentl …
- 20.5k
6
votes
Does smoothness descend along flat morphisms?
Here's a direct reference:
Hochster Math 615 - 2004, February 18th
It's a corollary of the characterization of regularity by the projective dimension of $R/m$.
I found this by tracking references f …
- 20.5k
5
votes
When can a finite map be blown up to a flat one?
Have you seen "Critères de platitude et de projectivité. Techniques de "platification'' d'un module" by Raynaud-Gruson (1971)? In particular 5.2.2. I think it is very close to what you want (this wa …
- 20.5k
3
votes
When can one extend a flat family from a subscheme to the whole scheme?
This is not going to help too much in your case, but we do have the following I think.
Suppose that we have a map $f : X \to Y$ which has a section (whose image we call $Y$ as well, as above), in oth …
- 20.5k