Timeline for Implications of the abc conjecture in Arakelov theory
Current License: CC BY-SA 2.5
4 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jul 28, 2010 at 13:59 | vote | accept | Anweshi | ||
| Jul 27, 2010 at 18:56 | comment | added | T.. | Certainly not. There are many external applications. However, I think it is true at this time that for every Diophantine (ie., in the number field case) consequence of theorems or conjectures in Arakelov/arithmetic geometry that also is a consequence of ABC, the implication from ABC never "factors through" the hard geometry, it bypasses the geometry formalism. It is possible that will change in the future, but in the present state of knowledge, the answer to your question about "factoring through" is that either no example is known or there is some big news that I missed. | |
| Jul 26, 2010 at 16:18 | comment | added | Anweshi | So are you implying that Mordell is essentially the only external application of Arakelov theory? | |
| Jul 25, 2010 at 19:31 | history | answered | T.. | CC BY-SA 2.5 |