English

Generalised Howe curves of genus five attaining the Serre bound

Algebraic Geometry 2024-12-05 v1

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, p^2 or p^3 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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Cite

@article{arxiv.2412.03071,
  title  = {Generalised Howe curves of genus five attaining the Serre bound},
  author = {Motoko Qiu Kawakita},
  journal= {arXiv preprint arXiv:2412.03071},
  year   = {2024}
}

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8 pages