Timeline for Is there a nice proof of the fact that there are (p-1)/24 supersingular elliptic curves in characteristic p?
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4 events
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| Jun 15, 2010 at 22:22 | comment | added | S. Carnahan♦ | Thanks, that is helpful. I should have thought of $\Delta$. | |
| Jun 15, 2010 at 21:25 | comment | added | Emerton | Whether or not this is completely correct as written, I think that one should think of the degree of $\omega$ as coming from the existence of the section $\Delta$ which is non-zero at all non-cuspidal points. | |
| Jun 15, 2010 at 21:24 | comment | added | Emerton | One could try to compute the degree of $\omega_P$ in the following way: $\omega_P^{\otimes 12}$ has a section, namely $\Delta$, which has zeroes precisely at the cusps. If we work over $(Ell)$ itself, there is a single cusp where it has a simple zero. But probably one has some phenomena of the following sort: the Tate curve corresponding to the cusp at infinity has automorphisms of order 2, and so the true (i.e. stack theoretic) order of vanishing there is 1/2. Hence deg $\omega^{\otimes 12} = 1/2$, and so deg $\omega = 1/24$. | |
| Jun 15, 2010 at 17:48 | history | answered | S. Carnahan♦ | CC BY-SA 2.5 |