Timeline for Image of the cuspidal subgroup of J_0(N) in J_1(N)
Current License: CC BY-SA 2.5
8 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Sep 27, 2010 at 17:42 | vote | accept | Soroosh | ||
| Sep 27, 2010 at 17:41 | comment | added | Soroosh | Thanks! This example was actually confusing me, and that clarifies the situation. | |
| Sep 27, 2010 at 13:06 | answer | added | user631 | timeline score: 5 | |
| Sep 27, 2010 at 12:15 | answer | added | JSE | timeline score: 2 | |
| Sep 27, 2010 at 11:28 | history | edited | Franz Lemmermeyer | CC BY-SA 2.5 |
added 4 characters in body
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| Sep 27, 2010 at 5:53 | comment | added | BCnrd | This can be made "explicit" in the special case $N=11$, for which both curves have genus 1. By moduli interpretation of cusps, $X_1(p)$ has $p-1$ geometric cusps: $(p-1)/2$ are rational points (the $p$-gon cusps) and $(p-1)/2$ are a single Galois orbit (the $1$-gon cusps, residue field $\mathbf{Q}(\zeta_p)^+$). Making $X_1(11)$ an elliptic curve using a rational cusp and $X_0(11)$ an elliptic curve using its image (the cusp $0$, not $\infty$!!), the deg-5 map $\pi$ has kernel given by the rat'l cusps: $\ker \pi = \mathbf{Z}/(5)$. Hence, dual map has kernel $\mu_5$, and $\mu_5(\mathbf{Q})=1$. | |
| Sep 27, 2010 at 3:30 | history | edited | Soroosh | CC BY-SA 2.5 |
there were incorrect claims in my original question. I removed those claims.
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| Sep 27, 2010 at 2:11 | history | asked | Soroosh | CC BY-SA 2.5 |