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Rational Points of Bounded Height on Weighted Projective Stacks by Darda, Ratko is a scholarly article available to read on EtoBox.

What is Rational Points of Bounded Height on Weighted Projective Stacks about?

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.

Author

Darda, Ratko

Published

2021

Language

EN