STNB2023(36th edition)

Linear quadratic Chabauty for integral points on even degree hyperelliptic curves


Stevan Gajović


The method of Chabauty and Coleman is a powerful method to determine rational points on curves which satisfy $r$<$g$, where $g$ is the genus of the curve and $r$ is the Mordell-Weil rank of its Jacobian over $\mathbb{Q}$. However, the original method crucially depends on the condition $r$<$g$. In this talk, we explain how we can use (Coleman-Gross) $p$-adic heights to obtain an analogous method to compute the integral points on certain even degree hyperelliptic curves satisfying $r=g$. We discuss extensions over (quadratic) number fields. This is joint work with Steffen Müller.


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