Timeline for Simultaneous rank jumping of elliptic curves over number fields
Current License: CC BY-SA 4.0
8 events
| when toggle format | what | by | license | comment | |
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| Feb 7, 2022 at 14:32 | comment | added | Ariel Weiss | When $p=2$, $K = \mathbb Q$, and $j(E_1)$ and $j(E_2)$ are not simultaneously $0$ or $1728$, then a positive answer follows form Theorem 4 of this paper. | |
| Jan 19, 2022 at 8:19 | history | edited | Ariyan Javanpeykar | CC BY-SA 4.0 |
edited title
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| Jan 19, 2022 at 8:13 | history | edited | Ariyan Javanpeykar | CC BY-SA 4.0 |
Improved body of text slightly
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| Jan 15, 2022 at 20:06 | comment | added | Ariyan Javanpeykar | In the linked paper, for $p\geq 5$, the author (Dave Mendes Da Costa) proves the required statement for an elliptic curve $E$ by showing that there is a higher genus curve $C$, a finite morphism $C\to E$ of degree $<p$ and a morphism $C\to \mathbb{P}^1_K$ of degree $p$. The answer to the question would be positive if we could find a higher genus curve $C$ such that there is a finite morphism $C\to E_1$ of degree $<p$, a finite morphism $C\to E_2$ of degree $<p$, and a finite morphism $C\to \mathbb{P}^1_K$ of degree $p$. | |
| Jan 15, 2022 at 0:54 | history | edited | Ariyan Javanpeykar | CC BY-SA 4.0 |
added 45 characters in body
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| Jan 15, 2022 at 0:54 | comment | added | Ariyan Javanpeykar | Yes, good point. The ranks are then equal of course. | |
| Jan 15, 2022 at 0:31 | comment | added | Jason Starr | The answer is also positive if the two elliptic curves are isogenous over $K$. | |
| Jan 15, 2022 at 0:22 | history | asked | Ariyan Javanpeykar | CC BY-SA 4.0 |