Timeline for Fermat's last theorem over larger fields
Current License: CC BY-SA 3.0
5 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Nov 25, 2014 at 17:06 | comment | added | Ariyan Javanpeykar | @Pablo I added some more details to my comment above. | |
| Nov 25, 2014 at 14:58 | comment | added | Pablo | @AriyanJavanpeykar I was not aware of this kind of argument, but I do not see how this can work. It is not clear from your answer which properties of $\mathbb{Q}^{\text{ab}}$ or of the curve you use. I think that there are examples of smooth projective curves with a finite set of points over an infinite extension of $\mathbb{Q}$. Please explain to which polynomials you apply HIT to clarify. | |
| Nov 25, 2014 at 14:50 | comment | added | Ariyan Javanpeykar | @Pablo I guess you are then already aware of what I wrote in my "answer", and that it doesn't work in fact (or does it?). | |
| Nov 25, 2014 at 14:49 | comment | added | Pablo | Dear Alex, I am familiar with the literature on large fields and with some of the people working on these things. The point is that some of these people think that this conjecture is false, even though were it true, the consequences would be far reaching - Shafarevich conjecture on the freeness of $\text{Gal}(\mathbb{Q}^{\text{ab}})$. The point is that there are almost no varieties for which the conjecture holds true (even for abelian varieties this is unknown). This is the reason I am asking this here for specific varieties to see if, even in very special cases, the conjecture shoul hold. | |
| Nov 25, 2014 at 14:35 | history | answered | Alex B. | CC BY-SA 3.0 |