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June 2022 On the maximality of hyperelliptic Howe curves of genus 3
Ryo Ohashi
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Kodai Math. J. 45(2): 282-294 (June 2022). DOI: 10.2996/kmj45206

Abstract

In this paper, we study a Howe curve $C$ in positive characteristic $p \geq 3$ which is of genus 3 and is hyperelliptic. We will show that if $C$ is superspecial, then its standard form is maximal or minimal over $\mathbf{F}_{p^2}$ without taking its $\mathbf{F}_{p^2}$-form.

Acknowledgment

This paper was written while the author was a Ph.D. student at Yokohama National University, and I would like to express my special thanks to my supervisor Prof. Shushi Harashita for his guidance. The author thanks Toshiyuki Katsura and Tomoyoshi Ibukiyama for their helpful comments.

Citation

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Ryo Ohashi. "On the maximality of hyperelliptic Howe curves of genus 3." Kodai Math. J. 45 (2) 282 - 294, June 2022. https://doi.org/10.2996/kmj45206

Information

Received: 31 January 2022; Revised: 1 March 2022; Published: June 2022
First available in Project Euclid: 30 June 2022

Digital Object Identifier: 10.2996/kmj45206

Subjects:
Primary: 14G05
Secondary: 14G17 , 14H45 , 14H50

Keywords: algebraic curve , maximal curve , positive characteristic , Superspecial curve

Rights: Copyright © 2022 Tokyo Institute of Technology, Department of Mathematics

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Vol.45 • No. 2 • June 2022
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