Timeline for Is there any theorem like implicit function theorem in $\mathbb{Q}$ ?
Current License: CC BY-SA 4.0
8 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Sep 10 at 17:02 | comment | added | Mohsen Shahriari | (... continued) consider $ Y = ( Y _ 1 , Y _ 2 ) $ and $ P ( X , Y ) = ( Y _ 1 - Y _ 2 ) X ^ 2 + X $, and the infinitely many choices you can make for the values of $ Y $ to make the $ X ^ 2 $ term vanish. Is there a way around this problem in the multivariate case? Can one get more information about the set of suitable $ a $ (for example them being Zariski dense, as the wiki page suggests) to make the argument also work for the multivariate case? | |
| Sep 10 at 17:02 | comment | added | Mohsen Shahriari | Since there are bars over the variables in the statement of the problem, I assume that the OP considers your $ Y $ as a (finite) sequence of variables. Unless $ Y $ is a single variable, I think that your argument is flawed, even if $ X $ is a single variable. The mere information that there are infinitely many $ a $'s for which $ P _ i ( X , a ) $ is irreducible does not imply that $ P _ i $ is of degree $ 1 $ in $ X $: (to be continued...) | |
| S Sep 9 at 12:20 | history | suggested | Mohsen Shahriari | CC BY-SA 4.0 |
removed extra parenthesis, removed the URL from text body
|
| Sep 9 at 10:29 | review | Suggested edits | |||
| S Sep 9 at 12:20 | |||||
| Oct 25, 2012 at 2:31 | comment | added | Luke | You are right. I have to change my question in the form P(Q(Y),Y)=0. Thank you! | |
| Oct 24, 2012 at 17:41 | history | edited | Laurent Berger | CC BY-SA 3.0 |
deleted 25 characters in body
|
| Oct 24, 2012 at 16:09 | history | edited | Laurent Berger | CC BY-SA 3.0 |
added 169 characters in body; added 36 characters in body
|
| Oct 24, 2012 at 16:02 | history | answered | Laurent Berger | CC BY-SA 3.0 |