Coverings of Curves of Genus 2

We shall discuss the idea of finding all rational points on a curve \(\mathcal{C}\) by first finding an associated collection of curves whose rational points cover those of \(\mathcal {C}\). This classical technique has recently been given a new lease of life by being combined with descent techniques on Jacobians of curves, Chabauty techniques, and the increased power of software to perform algebraic number theory. We shall survey recent applications during the last 5 years which have used Chabauty techniques and covering collections of curves of genus 2 obtained from pullbacks along isogenies on their Jacobians.

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