An upper bound on the number of rational points of arbitrary projective varieties over finite fields

DOI10.1090/proc/13015zbMath1369.11044arXiv1409.7544OpenAlexW2951883094MaRDI QIDQ2814392

Alain Couvreur

Publication date: 22 June 2016

Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1409.7544

zbMATH Keywords

finite fieldbound of number of rational points

Mathematics Subject Classification ID

Rational points (14G05) Finite ground fields in algebraic geometry (14G15) Varieties over finite and local fields (11G25)

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Arithmetic, Geometry, and Coding Theory: Homage to Gilles Lachaud ⋮ Number of solutions of systems of homogeneous polynomial equations over finite fields ⋮ Bounds on the number of rational points of algebraic hypersurfaces over finite fields, with applications to projective Reed-Muller codes ⋮ A Bertini type theorem for pencils over finite fields ⋮ Remarks on the Tsfasman-Boguslavsky Conjecture and higher weights of projective Reed-Muller codes ⋮ Transverse linear subspaces to hypersurfaces over finite fields ⋮ Vanishing ideals of projective spaces over finite fields and a projective footprint bound ⋮ On two upper bounds for hypersurfaces involving a Thas' invariant ⋮ Maximum Number of Common Zeros of Homogeneous Polynomials over Finite Fields ⋮ On a Homma-Kim conjecture for nonsingular hypersurfaces

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