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May 5, 2021 at 16:27 vote accept AVP82000
May 5, 2021 at 8:56 answer added Jef timeline score: 4
May 5, 2021 at 2:52 comment added Felipe Voloch $J(C)_{\Theta}[n]$ is a curve. The map $D \mapsto nD$ describes it as an étale cover of $\Theta$ of degree $n^2$. To compute the intersection we have to know the algebraic equivalence class of the two curves with $m$ and $n$. My guess is that this curve is algebraically equivalent to $n\Theta$ but I haven't checked that. If that's the case, the intersection will have $2mn$ points.
May 4, 2021 at 19:29 comment added Joe Silverman Have your tried searching on "uniform Manin-Mumford conjecture" or "uniform Raynaud's theorem"?
May 4, 2021 at 19:17 history edited AVP82000 CC BY-SA 4.0
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Apr 21, 2021 at 14:45 history asked AVP82000 CC BY-SA 4.0