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arXiv · 2106.10120

Rational points of bounded height on weighted projective stacks

Ratko Darda
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Abstract

A weighted projective stack is a stacky quotient $\mathscr P(\mathbf a)=(\mathbf A^n-\{0\})/\mathbb G_m$, where the action of $\mathbb G_m$ is with weights $\mathbf a\in\mathbb Z^n_{>0}$. Examples are: the compactified moduli stack of elliptic curves $\mathscr P(4,6)$ and the classifying stack of $\mu_m$-torsors $B\mu_m=\mathscr P(m)$. We define heights on the weighted projective stacks. The heights generalize the naive height of an elliptic curve and the absolute discriminant of a torsor. We use the heights to count rational points. We find the asymptotic behaviour for the number of rational points of bounded heights.

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Ratko Darda. 2021-06-18. Rational points of bounded height on weighted projective stacks. https://arxiv.org/abs/2106.10120

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