Timeline for Smooth surjective morphism to integral scheme
Current License: CC BY-SA 4.0
5 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Nov 11, 2022 at 16:09 | comment | added | Piotr Achinger | In fact Stacks Project, Lemma 06DM implies that "geometrically unibranch" is equivalent to "etale locally irreducible". | |
| Nov 11, 2022 at 16:05 | comment | added | Piotr Achinger | See Hartshorne "Algebraic Geometry" Chapter III, Exercise 10.6 | |
| Nov 11, 2022 at 16:01 | comment | added | ofiz | Are you saying that there is an étale morphism $f : X \rightarrow Y$, where $Y$ is the node, such that $X$ connected, yet reducible? If so, is it trivial to construct it? Thank you | |
| Nov 11, 2022 at 15:30 | comment | added | Piotr Achinger | The node is not etale locally irreducible. So the answer to your question is negative outside the geometrically unibranch case. | |
| Nov 11, 2022 at 15:26 | history | asked | ofiz | CC BY-SA 4.0 |