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arXiv · 2306.02718

Complete intersections of cubic and quadric hypersurfaces over $\mathbb{F}_q(t)$

Jakob Glas
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Abstract

Using a two-dimensional version of the delta method, we establish an asymptotic formula for the number of rational points of bounded height on non-singular complete intersections of cubic and quadric hypersurfaces of dimension at least $23$ over $\mathbb{F}_q(t)$, provided $\text{cha}(\mathbb{F}_q)>3$. Under the same hypotheses, we also verify weak approximation.

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Jakob Glas. 2023-06-05. Complete intersections of cubic and quadric hypersurfaces over $\mathbb{F}_q(t)$. https://arxiv.org/abs/2306.02718

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