Rational points of bounded height on weighted projective stacks

2021/06/18 by Darda, Ratko · 1 citation
#FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2106.10120

Abstract

A weighted projective stack is a stacky quotient \mathscr P(\mathbf a)=(\mathbf Aⁿ-\0\)/\mathbb G_m, where the action of \mathbb G_m is with weights \mathbf a∈\mathbb Zⁿ_>0. Examples are: the compactified moduli stack of elliptic curves \mathscr P(4,6) and the classifying stack of μ_m-torsors Bμ_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.

Cited by

• Arithmetic Sparsity and Obstructions in Weighted Projective Spaces

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