Timeline for Is this finite surjective flat morphism of 2 dimensional schemes a local complete intersection
Current License: CC BY-SA 2.5
13 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Oct 4, 2010 at 12:31 | history | edited | Francesco Polizzi | CC BY-SA 2.5 |
added 7 characters in body
|
| Oct 4, 2010 at 12:06 | comment | added | Angelo | Sorry, I withdraw my statement that $Y$ should always be l.c.i. in characteristic 0, I was confused, as it ofter happens. | |
| Oct 4, 2010 at 11:00 | history | edited | Francesco Polizzi | CC BY-SA 2.5 |
added 12 characters in body; added 16 characters in body; added 2 characters in body
|
| Oct 4, 2010 at 10:55 | history | edited | Francesco Polizzi | CC BY-SA 2.5 |
added 690 characters in body; added 77 characters in body
|
| Oct 4, 2010 at 10:05 | history | edited | Francesco Polizzi | CC BY-SA 2.5 |
added 135 characters in body; deleted 3 characters in body
|
| Oct 4, 2010 at 10:04 | comment | added | Francesco Polizzi | Oh, I see. I misread the question and I missed the requirement that $D$ should be simple normal crossing. Thank you for pointing it out, I will edit the answer. | |
| Oct 4, 2010 at 9:46 | comment | added | Angelo | To Francesco: A curve on a surface is a normal crossing divisor when it has nodal singularities, thus cannot have more than two branches through each point. | |
| Oct 4, 2010 at 9:40 | history | edited | Francesco Polizzi | CC BY-SA 2.5 |
edited body
|
| Oct 4, 2010 at 9:38 | comment | added | Francesco Polizzi | @Angelo: I checked the construction and I found no errors. Maybe I'm missing something, but I do not understand exactly what. How do you exactly use Abhyankar's lemma to prove that $Y$ must be lci? As far as I know, it says that I can get rid of (tame) ramification by taking a finite, branched cover $Z \to \mathbb{P}^2$... | |
| Oct 4, 2010 at 9:27 | comment | added | Ariyan Javanpeykar | @Angelo: I'm a bit confused. Does your statement imply that if X is fibered over a Dedekind scheme B with function field K(B) of characteristic zero, the morphism \pi is a local complete intersection (in the sense of Liu Section 4.6.2)? | |
| Oct 4, 2010 at 9:19 | comment | added | Angelo | I am afraid that your $D$ is not a normal crossing divisor. In characteristic 0 the scheme $Y$ should always be l.c.i., because of Abhyankar's Lemma. | |
| Oct 4, 2010 at 9:03 | history | edited | Francesco Polizzi | CC BY-SA 2.5 |
added 197 characters in body; added 40 characters in body
|
| Oct 4, 2010 at 8:57 | history | answered | Francesco Polizzi | CC BY-SA 2.5 |