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A proof of the Hasse-Weil inequality for genus 2 à la Manin. (English) Zbl 1441.11158

Summary: We prove the Hasse-Weil inequality for genus 2 curves given by an equation of the form \(y^2 = f(x)\) with \(f\) a polynomial of degree 5, using arguments that mimic the elementary proof of the genus 1 case obtained by Yu. I. Manin in [Izv. Akad. Nauk SSSR, Ser. Mat. 20, 673–678 (1956; Zbl 0072.03202)].

MSC:

11G10 Abelian varieties of dimension \(> 1\)
11G20 Curves over finite and local fields
14G10 Zeta functions and related questions in algebraic geometry (e.g., Birch-Swinnerton-Dyer conjecture)
14G15 Finite ground fields in algebraic geometry

Citations:

Zbl 0072.03202
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Full Text: DOI arXiv

References:

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