Dichotomous point counts over finite fields

Victor Y. Wang

doi:10.1016/j.jnt.2023.03.001

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arXiv · 2202.10427

Dichotomous point counts over finite fields

Victor Y. Wang

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Abstract

We establish a near dichotomy between randomness and structure for the point counts of arbitrary projective cubic threefolds over finite fields. Certain "special" subvarieties, not unlike those in the Manin conjectures, dominate. We also prove new general results for projective hypersurfaces. Our work continues a line of inquiry initiated by Hooley.

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Victor Y. Wang. 2022-02-21. Dichotomous point counts over finite fields. https://doi.org/10.1016/j.jnt.2023.03.001

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