Timeline for How fast can elliptic curve rank grow in towers of number fields?
Current License: CC BY-SA 4.0
4 events
| when toggle format | what | by | license | comment | |
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| Dec 13, 2023 at 16:28 | comment | added | Chris Wuthrich | The minimalistic conjecture for a $2$-group would only imply that the rank is 100% of the times less than the degree. The 50/50 is not generally true in all quadratic extensions as seen in arxiv.org/abs/0802.4027 | |
| Dec 13, 2023 at 14:53 | comment | added | David Lampert | Thanks @Chris Wuthrich. The $\mathbb{Z}_p$-extensions example of Cornut and Vatsal beats my example for rank growth and I'll look at the videos. For a quadratic extension $F/\mathbb{Q}$ should the minimalist conjecture say $$\DeclareMathOperator{\rank}{rank}\rank E(F) - \rank E(\mathbb{Q}) < 2 $$ for 100% of $E/\mathbb{Q}$ since it's conjectured 50% of elliptic curves over $\mathbb{Q}$ have rank 0 and 50% have rank 1? Given a tower of quadratic extensions, would you guess that for 100% of elliptic curves over the base, the rank increases by 0 in 50% of the extensions and by 1 in 50%? | |
| Dec 13, 2023 at 14:45 | vote | accept | David Lampert | ||
| Dec 13, 2023 at 9:28 | history | answered | Chris Wuthrich | CC BY-SA 4.0 |