Dichotomous point counts over finite fields

DOI10.1016/j.jnt.2023.03.001arXiv2202.10427OpenAlexW4366496778MaRDI QIDQ6101535

Victor Y. Wang

Publication date: 1 June 2023

Published in: Journal of Number Theory (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2202.10427

zbMATH Keywords

finite fieldsdiscriminantsdichotomiespoint countsvarieties of low degree

Mathematics Subject Classification ID

Singularities in algebraic geometry (14B05) Complete intersections (14M10) Varieties of low degree (14N25) Varieties over finite and local fields (11G25)

Cites Work

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• Homogeneity degrees of the set of singular complete intersections
• The determinant and the discriminant of a complete intersection of even dimension
• On the number of points on a complete intersection over a finite field. (Appendix: Number of points on singular complete intersections by Nicholas M. Katz)
• Betti numbers of hypersurfaces and defects of linear systems
• Complete intersections on general hypersurfaces
• Exponential sums, the geometry of hyperplane sections, and some diophantine problems
• The discriminant and the determinant of a hypersurface of even dimension
• Representation of squares by nonsingular cubic forms
• Maximal families of nodal varieties with defect
• Hypersurfaces with defect
• Rational Points on Varieties
• Flops on holomorphic symplectic fourfolds and determinantal cubic hypersurfaces
• Corrado Segre and Nodal Cubic Threefolds
• On Waring's problem
• Sums of Betti numbers in arbitrary characteristic.

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