Rational points on complete intersections of cubic and quadric hypersurfaces over Fq(t)

Glas, Jakob

Rational points on complete intersections of cubic and quadric hypersurfaces over Fq(t)

Glas J. 2024. Rational points on complete intersections of cubic and quadric hypersurfaces over Fq(t). Journal of the London Mathematical Society. 110(4), e12991.

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DOI

10.1112/jlms.12991

Journal Article | Published | English

Scopus indexed

Author

Glas, Jakob^ISTA

Corresponding author has ISTA affiliation

Department

Browning Group

Grant

Rational curves via function field analytic number theory

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 Fq(t), provided char (Fq)>3. Under the same hypotheses, we also verify weak approximation.

Publishing Year

2024

Date Published

2024-10-01

Journal Title

Journal of the London Mathematical Society

Publisher

London Mathematical Society

Acknowledgement

The author would like to thank his supervisor Tim Browning for suggesting this project and many helpful conversations and Pankaj Vishe for useful comments. Moreover, he is grateful to Dante Bonolis and Julian Lyczak for sharing their expertise in exponential sums and geometry. While working on this paper, the author was supported by FWF grant (DOI 10.55776/P36278).

Volume

110

Issue

Article Number

e12991

ISSN

0024-6107

eISSN

1469-7750

IST-REx-ID

18173

Cite this

Glas J. Rational points on complete intersections of cubic and quadric hypersurfaces over Fq(t). Journal of the London Mathematical Society. 2024;110(4). doi:10.1112/jlms.12991

Glas, J. (2024). Rational points on complete intersections of cubic and quadric hypersurfaces over Fq(t). Journal of the London Mathematical Society. London Mathematical Society. https://doi.org/10.1112/jlms.12991

Glas, Jakob. “Rational Points on Complete Intersections of Cubic and Quadric Hypersurfaces over Fq(T).” Journal of the London Mathematical Society. London Mathematical Society, 2024. https://doi.org/10.1112/jlms.12991.

J. Glas, “Rational points on complete intersections of cubic and quadric hypersurfaces over Fq(t),” Journal of the London Mathematical Society, vol. 110, no. 4. London Mathematical Society, 2024.

Glas J. 2024. Rational points on complete intersections of cubic and quadric hypersurfaces over Fq(t). Journal of the London Mathematical Society. 110(4), e12991.

Glas, Jakob. “Rational Points on Complete Intersections of Cubic and Quadric Hypersurfaces over Fq(T).” Journal of the London Mathematical Society, vol. 110, no. 4, e12991, London Mathematical Society, 2024, doi:10.1112/jlms.12991.

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