Rational points on hyperelliptic curves : recent developments

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Stoll, Michael:
Rational points on hyperelliptic curves : recent developments.
In: Computeralgebra-Rundbrief. Bd. 54 (2014) . - S. 10-13.
ISSN 0933-5994

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Abstract

We give an overview over recent results concerning rational points on hyperelliptic curves. One result says that ‘most’ hyperelliptic curves of high genus have very few rational points. Another result gives a bound on the number of rational points in terms of the genus and the Mordell-Weil rank, provided the latter is sufficiently small. The first result relies on work by Bhargava and Gross on Selmer groups of hyperelliptic Jacobians, and both results use Chabauty’s method.