Generalised Howe curves of genus five attaining the Serre bound

2024/12/04 by Kawakita, Motoko Qiu
#11G20 #14G05 #14G50 #Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2412.03071

Abstract

We find that non-hyperelliptic generalised Howe curves and their twists of genus 5 attain the Hasse-Weil-Serre bound over some finite fields of order p, p² or p³ for a prime p. We are able to decompose their Jacobians completely under certain assumptions and to determine the precise condition on the finite field over which they attain the Hasse-Weil-Serre bound.

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