Timeline for Consequences of the Birch and Swinnerton-Dyer Conjecture?
Current License: CC BY-SA 3.0
10 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Mar 31, 2017 at 19:58 | comment | added | Greg Martin | Some computational questions about points on elliptic curves, as well as statements about elliptic curves on average, are rather easier to approach on the $L$-function side (assuming BSD is true) than on the elliptic curve side. | |
| Mar 31, 2017 at 17:51 | comment | added | KRyan | Please do not use code formatting for anything but actual code. Code formatting is first-and-foremost a semantic declaration, that the text is code. For visual browsers, that usually means monospace font and a gray background, but for non-traditional browsers, e.g. screen-readers for the blind, something else must be done to make code understandable. This often makes the text difficult to understand if it isn't code—reading letter-by-letter is not unheard of, for example. Please be considerate of accessibility and use code formatting appropriately! | |
| Mar 31, 2017 at 17:49 | history | edited | KRyan | CC BY-SA 3.0 |
do not use code formatting for anything but code, it is bad for accessibility
|
| Mar 31, 2017 at 13:29 | history | made wiki | Post Made Community Wiki by Todd Trimble | ||
| Mar 31, 2017 at 3:27 | answer | added | Kimball | timeline score: 12 | |
| Mar 31, 2017 at 1:15 | comment | added | Pasten | Ram Murty and I recently showed that if elliptic curves over number fields have an automorphic L-function and if the rank part of twisted BSD holds, then Hilbert's tenth problem for the ring of integers of any number field is undecidable (actually we require less, but this formulation fits into a comment). Alternatively, by Mazur-Rubin one knows that finiteness of Sha would have the same consequence. | |
| Mar 31, 2017 at 0:51 | answer | added | Joe Silverman | timeline score: 21 | |
| Mar 30, 2017 at 21:31 | comment | added | Yonatan Harpaz | This is probably not the kind of consequences you're looking for, but it is worthwhile to note that the Birch and Swinnerton-Dyer conjecture contains as a "mere" prerequisite the assertion that the Tate-Shafarevich group of elliptic curves is finite. This conjectural claim is of huge importance as it implies that global duality theory for elliptic curves (or abelian varieties in general) is well behaved. There are quite a lot of results in arithmetic geometry which are conditional on that fact. | |
| Mar 30, 2017 at 21:05 | comment | added | Sylvain JULIEN | Try to google 'congruent number bsd' to get a consequence of this conjecture. | |
| Mar 30, 2017 at 21:00 | history | asked | mathphys | CC BY-SA 3.0 |