Timeline for Deformation theory over the field of algebraic numbers
Current License: CC BY-SA 2.5
16 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jan 10, 2011 at 15:50 | vote | accept | Hugo Chapdelaine | ||
| Jan 10, 2011 at 15:50 | history | bounty ended | Hugo Chapdelaine | ||
| Jan 7, 2011 at 20:00 | answer | added | user10849 | timeline score: 2 | |
| Jan 7, 2011 at 12:39 | answer | added | naf | timeline score: 4 | |
| Jan 7, 2011 at 2:12 | answer | added | Felipe Voloch | timeline score: 3 | |
| Jan 7, 2011 at 1:22 | history | bounty started | Hugo Chapdelaine | ||
| Jan 5, 2011 at 3:50 | comment | added | Hugo Chapdelaine | Well in general we have the following result: Thm (a) Let $Y$ be a quasi-projective variety defined over $\overline{\mathbf{Q}}$ and let $f:X\rightarrow Y$ be an finite etale morphism defined over $\mathbf{C}$ then $X$ can be defined over $\overline{\mathbf{Q}}$. One direction of Belyi's theorem is a special case of Thm (a) above when you take $Y=P^1-\{0,1,\infty\}$. I guess that the "tentative theorem" of the question readily implies Thm (a). | |
| Jan 4, 2011 at 19:32 | comment | added | Makhalan Duff | How would this fit with Belyi's theorem in the dimension=1 case? | |
| Jan 4, 2011 at 19:27 | history | edited | Hugo Chapdelaine | CC BY-SA 2.5 |
added 60 characters in body
|
| Jan 2, 2011 at 20:25 | comment | added | Hugo Chapdelaine | Yes there might be some algebraic relations but I don't think it is a problem. I should probably rephrase the question in terms of derivations of $\mathbb{C}$ over $\overline{\mathbb{Q}}$. thanks for your comment. | |
| Jan 2, 2011 at 17:06 | comment | added | Qfwfq | What if there are algebraic relations between the various coefficients $t_i$? | |
| Dec 31, 2010 at 2:40 | comment | added | Hugo Chapdelaine | If $Y$ is a variety over a field $K$ of characteristic $0$ then by definition it is of finite type over $Spec(K)$. So any such variety may be viewed a scheme over $Spec(\mathbb{Q}[t_1,\ldots,t_n])$ where the $t_i$'s are the various coefficients which appear in a choice of a set of defining equations of $Y$. | |
| Dec 31, 2010 at 2:36 | comment | added | Hugo Chapdelaine | By a model of a variety $X$ over a field $K$ I simply mean that $X$ may be defined as the zero locus of a bunch of polynomials with coefficients in $K$. | |
| Dec 30, 2010 at 22:25 | comment | added | Qfwfq | Also, what do you mean by "spreading out $X_0$" ? | |
| Dec 30, 2010 at 22:22 | comment | added | Qfwfq | Maybe my commnet is too naif and maybe I didn't get the point, but: isn't Lefschez principle sufficient to say that any complex variety has a "model" over any algebraically closed field of characteristic zero? What's the definition of "having a model over the algebraic numbers"? | |
| Dec 30, 2010 at 3:46 | history | asked | Hugo Chapdelaine | CC BY-SA 2.5 |