Timeline for Why all supersingular elliptic curves over $\bar{\mathbb{F}_p}$ are isogenous?
Current License: CC BY-SA 4.0
8 events
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| Apr 19, 2023 at 9:28 | comment | added | HaomengXu | @djao Thanks for your guidance and patient to my naive question. I just found out that you mentioned this in "2.2 Isogeny graphs" of the thesis "Towards quantum-resistant cryptosystems from ssEC isogenies". I read the thesis a few months ago, but didn't connect it to this problem. In a word, I learned a lot from your answer, thank you again for inspire and help. | |
| Apr 17, 2023 at 0:13 | comment | added | djao | I don't think it's substantially easier to prove connectedness than Ramanujan using this approach. You need a bound on the growth of the coefficients of cusp forms in any case. One could view the Ramanujan conjecture as a sort of Riemann hypothesis, and under this view, connectedness is analogous to proving the existence of a zero-free region whereas the Ramanujan property is like the full on Riemann hypothesis. | |
| Apr 16, 2023 at 18:13 | comment | added | Watson | (By the way, the Ramanujan property is nicely sketched in the document: "Enric Florit - Random walks on supersingular isogeny graphs") | |
| Apr 16, 2023 at 17:54 | comment | added | Watson | Nice! Is there an easy way to see that the $\ell$-isogeny superingular graph is connected? (I would need to look at Corollary 77 in D. Kohel's thesis...). | |
| Apr 16, 2023 at 12:21 | vote | accept | HaomengXu | ||
| Apr 16, 2023 at 12:50 | |||||
| Apr 16, 2023 at 8:20 | history | edited | djao | CC BY-SA 4.0 |
added 22 characters in body
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| S Apr 16, 2023 at 8:14 | review | First answers | |||
| Apr 16, 2023 at 8:38 | |||||
| S Apr 16, 2023 at 8:14 | history | answered | djao | CC BY-SA 4.0 |