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What is the quotient $E \!\times\! E^\prime / G$?

I claim that $E\times E'/G$ is the Weil restriction of $E_{\mathbb{F}_{p^2}}$ w.r.t. $\mathbb{F}_{p^2}/\mathbb{F}_{p}$. (I don't know about the product question, or the Jacobian question; the answers …
Laurent Moret-Bailly's user avatar
4 votes

Non trivial family of hyperelliptic curves

Apart from the nice answer by abx, one can also argue as follows: the obvious commutative diagram $$\begin{array}{rcl} X\times S & \longrightarrow & (X\times S)/(f\times g) \\ \mathrm{pr}_2\downarrow …
Laurent Moret-Bailly's user avatar