Timeline for Why is the kernel cyclic if and only if the walk does not backtrack?
Current License: CC BY-SA 4.0
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| when toggle format | what | by | license | comment | |
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| Jan 9, 2023 at 9:08 | comment | added | Ben Smith | If you backtrack then you are using the dual isogeny of the previous step; the composition is $[\ell_A]$, which has non-cyclic kernel. Similarly, if you have a non-cyclic kernel of order $\ell_A^{e_A}$ that is not cyclic, then it contains a subgroup isomorphic to $(\mathbb{Z}/(\ell_A))^2$, so you can factor $[\ell_A]$ out of the isogeny - and this represents a backtracking step. | |
| S Jan 8, 2023 at 14:58 | review | First questions | |||
| Jan 9, 2023 at 9:58 | |||||
| S Jan 8, 2023 at 14:58 | history | asked | Manuel Bravi | CC BY-SA 4.0 |