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arXiv · 2201.10624

Points of bounded height in images of morphisms of weighted projective stacks with applications to counting elliptic curves

Tristan Phillips
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Abstract

Asymptotics are given for the number of rational points in the domain of a morphism of weighted projective stacks whose images have bounded height and satisfy a (possibly infinite) set of local conditions. As a consequence we obtain results for counting elliptic curves over number fields with prescribed level structures, including the cases of $Γ(N)$ for $N\in\{1,2,3,4,5\}$, $Γ_1(N)$ for $N\in\{1,2,\dots,10,12\}$, and $Γ_0(N)$ for $N\in\{1,2,4,6,8,9,12,16,18\}$. In all cases we give an asymptotic with an expression for the leading coefficient, and in many cases we also give a power-saving error term.

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Tristan Phillips. 2026-03-23. Points of bounded height in images of morphisms of weighted projective stacks with applications to counting elliptic curves. https://doi.org/10.1112/jlms.70486

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