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

Jakob Glas

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

Number Theory 2023-06-06 v1

Authors: Jakob Glas

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.

Keywords

complete intersections cubic hypersurfaces quadric hypersurfaces rational points delta method weak approximation function fields

Cite

@article{arxiv.2306.02718,
  title  = {Complete intersections of cubic and quadric hypersurfaces over $\mathbb{F}_q(t)$},
  author = {Jakob Glas},
  journal= {arXiv preprint arXiv:2306.02718},
  year   = {2023}
}

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49 pages

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