Timeline for flat and finite type morphisms

9 events

when toggle format	what		by	license	comment
Jun 23, 2013 at 17:41	vote	accept	prochet
Jun 23, 2013 at 16:14	history	edited	Jason Starr	CC BY-SA 3.0	Incorporated comments
Jun 23, 2013 at 16:00	comment	added	Karl Schwede		The same trick will work for things over a field. You can let $Y = \text{Spec }k[x]$ and $X = \text{Spec }(k[x] \oplus k(x) )$. $$\text{ }$$ The map $k[x] \to k[x] \oplus k(x)$ is the natural one on each coordinate. All the fibers are finite type, but the map is not finite type. It is also clearly flat.
Jun 23, 2013 at 15:59	comment	added	S. Carnahan♦		Standard dictionary: change $\mathbb{Z}$ to $k[t]$ and $\mathbb{Q}$ to $k(t)$.
Jun 23, 2013 at 15:10	vote	accept	prochet
Jun 23, 2013 at 15:10
Jun 23, 2013 at 15:10	comment	added	prochet		it's not over a field. Sorry, I omit to precise but $k$ is a field.
Jun 23, 2013 at 15:09	vote	accept	prochet
Jun 23, 2013 at 15:10
Jun 23, 2013 at 15:07	vote	accept	prochet
Jun 23, 2013 at 15:09
Jun 23, 2013 at 14:59	history	answered	Jason Starr	CC BY-SA 3.0