Timeline for Can arithmetic geometry accelerate the search for rational points in high dimensions?
Current License: CC BY-SA 4.0
8 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Feb 21, 2021 at 17:20 | comment | added | Daniel Loughran | So you are looking for algorithms? This is not at all clear from your question. Can you please clarify exactly what you are after? | |
| Feb 21, 2021 at 12:56 | review | Close votes | |||
| Feb 26, 2021 at 3:07 | |||||
| Feb 21, 2021 at 12:51 | comment | added | Grigore Milli | @DanielLoughran I think many techniques used in this field do not yield clear algorithms so I personally do not feel it is too broad. The second trick is not terribly ingenious but it is there and I think if I did not point it out somebody else would. | |
| Feb 21, 2021 at 12:37 | comment | added | Daniel Loughran | This question is way too broad. The vast majority of the modern study of rational points is about trying to use tools from algebraic geometry to understand them. Also your second trick (taking sums of squares) is completely useless and I have never seen a genuine application of this method. | |
| Feb 21, 2021 at 11:55 | comment | added | Daebeom Choi | There is a conjecture called Bombieri-Lang conjecture, which is a higher-dimensional analogue of Faltings's theorem. Although this conjecture is largely open, some special cases are proved. See this question. | |
| Feb 21, 2021 at 10:59 | comment | added | Wojowu | I know the theory of Heegner points can allow you to find points on elliptic curves. It may have analogues in higher dimensions - it is probably highly conjectural, but may be something that works in practice | |
| Feb 21, 2021 at 10:25 | review | First posts | |||
| Feb 21, 2021 at 12:08 | |||||
| Feb 21, 2021 at 10:21 | history | asked | Grigore Milli | CC BY-SA 4.0 |