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A bound on the number of points of a plane curve. (English) Zbl 1185.14017
Summary: A conjecture is formulated for an upper bound on the number of points in PG\((2,q)\) of a plane curve without linear components, defined over GF\((q)\). We prove a new bound which is half-way from the known bound to the conjectured one. The conjecture is true for curves of low or high degree, or with rational singularity.

14G15 Finite ground fields in algebraic geometry
14H25 Arithmetic ground fields for curves
Full Text: DOI
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