Rational points of bounded height on weighted projective stacks
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...
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| Main Author | |
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| Format | Journal Article |
| Language | English |
| Published |
18.06.2021
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| Subjects | |
| Online Access | Get full text |
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| Summary: | 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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| DOI: | 10.48550/arxiv.2106.10120 |