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arXiv · 2606.06327

Arithmetic statistics of isogeny Selmer groups associated to hyperelliptic curves

Martí Oller
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Abstract

We determine asymptotic results for the average size of Selmer groups arising from certain isogenies related to Jacobians of hyperelliptic curves of genus $g\geq 2$. Our results come from two different routes. The first route is through the geometry-of-numbers methods pioneered by Bhargava, where we obtain new parametrisations coming from Vinberg theory arising from representations related to the Dynkin diagrams of type $B$ and $C$. The second route uses recent results by Koymans--Smith, which relate the average sizes of Selmer groups to Tamagawa ratios through a formula by Greenberg--Wiles.

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Martí Oller. 2026-09-17. Arithmetic statistics of isogeny Selmer groups associated to hyperelliptic curves. https://arxiv.org/abs/2606.06327

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