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On the existence of curves with prescribed a-number

Zijian Zhou College of Liberal Arts and Sciences, National University of Defense Technology, Changsha, China

Number Theory Algebraic Geometry mathscidoc:2203.24002

Arkiv for Matematik, 59, (1), 229-246, 2021.5
We study the existence of Artin–Schreier curves with large a‑number. We show that Artin–Schreier curves with large a‑number can be written in certain forms and discuss their supersingularity. We also give a basis of the de Rham cohomology of Artin–Schreier curves. By computing the rank of the Hasse–Witt matrix of the curve, we also give bounds on the a‑number of trigonal curves of genus 5 in small characteristic.
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@inproceedings{zijian2021on,
  title={On the existence of curves with prescribed a-number},
  author={Zijian Zhou},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20220311105015448981959},
  booktitle={Arkiv for Matematik},
  volume={59},
  number={1},
  pages={229-246},
  year={2021},
}
Zijian Zhou. On the existence of curves with prescribed a-number. 2021. Vol. 59. In Arkiv for Matematik. pp.229-246. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20220311105015448981959.
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