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3
votes
Accepted
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 …
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 …