Dichotomous point counts over finite fields
Victor Y. Wang
TL;DR
This paper explores the distribution of point counts on projective cubic threefolds over finite fields, revealing a dichotomy between randomness and structure, and introduces new results for hypersurfaces.
Contribution
It establishes a near dichotomy for point counts on cubic threefolds and general hypersurfaces, highlighting the influence of special subvarieties.
Findings
Identification of a dichotomy between randomness and structure in point counts
Dominance of special subvarieties in point count distributions
New general results for projective hypersurfaces
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.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsAnalytic Number Theory Research · Algebraic Geometry and Number Theory · Limits and Structures in Graph Theory