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- W3014033499 abstract "In this article we prove several new uniform upper bounds on the number of points of bounded height on varieties over $mathbb{F}_q[t]$. For projective curves, we prove the analogue of Walsh' result with polynomial dependence on $q$ and the degree $d$ of the curve. For affine curves, this yields an improvement to bounds by Sedunova, and Cluckers, Forey and Loeser. In higher dimensions, we prove a version of dimension growth for hypersurfaces of degree $dgeq 64$, building on work by Castryck, Cluckers, Dittmann and Nguyen in characteristic zero. These bounds depend polynomially on $q$ and $d$, and it is this dependence which simplifies the treatment of the dimension growth conjecture." @default.
- W3014033499 created "2020-04-03" @default.
- W3014033499 creator A5071486927 @default.
- W3014033499 date "2020-03-24" @default.
- W3014033499 modified "2023-09-27" @default.
- W3014033499 title "Points of bounded height on curves and the dimension growth conjecture over $mathbb{F}_q[t]$" @default.
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