Let E/S be an elliptic curve, where S is any scheme. Must there exist a scheme $S'$, etale and surjective over $S$, such that the pullback $E' := E\times_S S'$ has infinitely (or even > 1) many sections over $S'$?
References would be appreciated.
2026-03-29 09:11:46.1774775506
does every elliptic curve E/S have infinitely many sections after passing to an etale extension of S?
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