scientific article; zbMATH DE number 7308132

zbMath1475.11002MaRDI QIDQ5149958

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Publication date: 9 February 2021

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zbMATH Keywords

finite fieldsrational pointsabelian varietiescurvesclass field theorygenus 2Golod-Shafarevich theoremasymptotic resultIhara constantgenus 3Deligne-Lusztig curvesexplicit formulas Weil's boundIhara's tower theoremOesterle's theoremSmyth's methodVoloch bound

Mathematics Subject Classification ID

Rational points (14G05) Research exposition (monographs, survey articles) pertaining to number theory (11-02) Curves over finite and local fields (11G20) Finite ground fields in algebraic geometry (14G15) Research exposition (monographs, survey articles) pertaining to algebraic geometry (14-02)

Related Items (10)

On abelian covers of the projective line with fixed gonality and many rational points ⋮ Ternary and Quaternary Curves of Small Fixed Genus and Gonality With Many Rational Points ⋮ Maximal curves and Tate-Shafarevich results for quartic and sextic twists ⋮ Optimal plane curves of degree \(q - 1\) over a finite field ⋮ Lower bounds on the maximal number of rational points on curves over finite fields ⋮ New sextics of genus 6 and 10 attaining the Serre bound ⋮ The maximum number of points on a curve of genus eight over the field of four elements ⋮ Relationships between hyperelliptic functions of genus 2 and elliptic functions ⋮ The relative class number one problem for function fields. I ⋮ Spanning the isogeny class of a power of an elliptic curve

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