Timeline for Computational tool for checking the existence of non-trivial rational zero of a cubic form
Current License: CC BY-SA 4.0
6 events
| when toggle format | what | by | license | comment | |
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| Dec 25, 2021 at 19:37 | comment | added | Daniel Loughran | If you have some specific example in mind there may be some hope | |
| Dec 25, 2021 at 19:36 | comment | added | Daniel Loughran | There is a vast literature on this and also quite a few mathoverflow posts. You can get quite far with just google. Try Poonen's book on rational points on varieties. In any case, the correct thing to check is $p$-adic solubility, not a solution in a finite field. | |
| Dec 25, 2021 at 7:50 | comment | added | Sky | Can you give me some reference of Hasse principle and Brauer Manin obstruction, also for which forms ,having non trivial real and finite field solution implies rational solutions. | |
| Dec 24, 2021 at 21:30 | comment | added | Daniel Loughran | In short, no. It is expected that the Brauer-Manin obstruction is the only one to the Hasse Principle in this case for smooth cubics, but this is an open problem. This obstruction is computable in principle. | |
| Dec 24, 2021 at 18:07 | history | edited | LSpice | CC BY-SA 4.0 |
Capitalise title; solution -> zero
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| Dec 24, 2021 at 15:16 | history | asked | Sky | CC BY-SA 4.0 |