2-coverings of Hyperelliptic Curves

In Ed Schaefer's talk, we have seen methods to bound the Mordell-Weil rank of hyperelliptic curves and, if this rank is low enough and we can actually find generators, Chabauty's method to get a good bound on the number of points. In this talk we will try to tackle the problem of finding the rational points on hyperelliptic curves when our first line of attack fails. We explicitly construct a family of unramified covers of a hyperelliptic curve, inspired by 2-descent on its Jacobian and we will discuss how one can decide local solvability for these curves and how one can do Chabauty-type computations on the curve.

Nils Bruin

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