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Pointless Hyperelliptic Curves, Ryan P. Becker, Darren B. Glass
Pointless Hyperelliptic Curves, Ryan P. Becker, Darren B. Glass
Math Faculty Publications
In this paper we consider the question of whether there exists a hyperelliptic curve of genus g which is defined over but has no rational points over for various pairs . As an example of such a result, we show that if p is a prime such that is also prime then there will be pointless hyperelliptic curves over of every genus.