Elliptic and Hyperelliptic Curves Over Supersimple Fields

It is proved that if $F$ is an infinite field with characteristic different from $2$ , whose theory is supersimple, and $C$ is an elliptic or hyperelliptic curve over $F$ with generic ‘modulus’, then $C$ has a generic $F$ -rational point. The notion of generity here is in the sense of the supersimple field $F$ .

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