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The characterization of Hermitian surfaces by the number of points. (English) Zbl 1410.11081
Summary: The nonsingular Hermitian surface of degree $${\sqrt{q} +1}$$ is characterized by its number of $${\mathbb{F}_q}$$ -points among the surfaces over $${\mathbb{F}_q}$$ of degree $${\sqrt{q} +1}$$ in the projective 3-space without $${\mathbb{F}_q}$$ -plane components.

##### MSC:
 11G25 Varieties over finite and local fields 14G15 Finite ground fields in algebraic geometry 14J70 Hypersurfaces and algebraic geometry
##### Keywords:
finite field; Hermitian surface; Weil-Deligne bound
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##### References:
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