Timeline for Evidence for the equivariant BSD conjecture with higher multiplicity
Current License: CC BY-SA 4.0
9 events
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| Jul 1 at 10:00 | history | edited | J M T P | CC BY-SA 4.0 |
(fixed a phrase that was too wordy)
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| Jun 17 at 11:27 | comment | added | Chris Wuthrich | Yes, there is the method .saturation. That works if the algorithm has found points that generate a subgroup of finite index. However over a large degree number field, it can very well happen that the heights of the generators are so large that the search won't find them. | |
| Jun 17 at 11:01 | vote | accept | J M T P | ||
| Jun 17 at 10:59 | comment | added | J M T P | @ChrisWuthrich Thank you for pointing that out! I went to check Simon's script, which is also used by the method '.gens()' in SageMath. But I'm puzzled by the following comment in SageMath's documentation: "Contrary to what the name of this method suggests, the points it returns do not always generate a subgroup of full rank in the Mordell-Weil group, nor are they necessarily linearly independent." So I wonder, can we still compute the RHS with that? Perhaps, in some cases, we can guarantee (by some other reason) that such is list of points is complete, and then we focus on these cases? | |
| Jun 14 at 21:00 | answer | added | David Loeffler | timeline score: 6 | |
| Jun 13 at 15:48 | comment | added | Chris Wuthrich | The sage question: Sage has Denis Simon's gp script for calculating the rank of elliptic curve over number fields, but the search for points is often more efficient using magma. It turns out this is often the hardest part of evaluating your right hand side. Once you have the points it is not hard to decompose it into irreducible factors using characters. But none is systematically implemented. | |
| Jun 13 at 15:45 | comment | added | Chris Wuthrich | Good question. I don't think there is a large amount of examples like this ever been computed or written down. I might have some, I will have to search for them. There is a folklore conjecture which states that ranks should be 100% of the time minimal (0 or 1 imposed by parity conditions), which will tell you that indeed it is rare to find examples of your kind. But over $\mathbb{Q}$ we also find rank $2$ curves. | |
| S Jun 13 at 15:33 | review | First questions | |||
| Jun 13 at 16:00 | |||||
| S Jun 13 at 15:33 | history | asked | J M T P | CC BY-SA 4.0 |