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Geometry-of-numbers over number fields and the density of ADE families of curves having squarefree discriminant

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arxiv 2505.11301 v1 pith:6JOP6OLA submitted 2025-05-16 math.NT

Martí Oller This is my paper
classification math.NT
keywords curvesdensitydiscriminantfamiliesfieldsgeometry-of-numbershavingnumber
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For families of curves arising from a Dynkin diagram of type ADE, we show that the density of such curves having squarefree discriminant is equal to the product of local densities. We do so using the framework of Thorne and Laga's PhD theses and geometry-of-numbers techniques developed by Bhargava, here expanded over number fields.

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  1. Geometry-of-numbers methods over global fields II: Coregular representations

    math.NT 2026-04 unverdicted novelty 7.0 of 10

    Geometry-of-numbers methods are extended to count orbits in coregular spaces over arbitrary global fields, yielding bounds on average ranks and Selmer sizes for elliptic curves and hyperelliptic Jacobians.

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