A proof of the Hasse-Weil inequality for genus 2 à la Manin

Abstract

We prove the Hasse-Weil inequality for genus 2 curves given by an equation of the form y2 = 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 1956.

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Correspondence to Eduardo Ruíz Duarte or Jaap Top.

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This author was supported by CONACyT México through the agreement CVU-440153

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Duarte, E.R., Top, J. A proof of the Hasse-Weil inequality for genus 2 à la Manin. Indian J Pure Appl Math 51, 761–776 (2020). https://doi.org/10.1007/s13226-020-0429-1

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Key words

  • Hasse-Weil inequality
  • hyperelliptic curve
  • genus two curve

2010 Mathematics Subject Classification

  • 11G10
  • 11G20
  • 14G10
  • 14G15