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On the a-number of Fermat type function fields and some of their subfields

  • Marie Frank vom Braucke
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Abstract

The a-number of a function field F is the dimension of the kernel of the Cartier operator acting on the holomorphic differentials of F. We compute the action of the Cartier operator on the holomorphic differentials on the Hermitian function field ℋ, function fields of Fermat type ℱn,m and the Hurwitz function field ℋn. From this, we obtain various results about the a-number of these function fields, including a generalisation of the results on the Fermat function field from Kodama and Washio.

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Cite

BibTeXRIS
BibTeX
@misc{braucke2026anumber,
  title = {{On the $a$-number of Fermat type function fields and some of their subfields}},
  author = {Marie Frank vom Braucke},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.08565},
  eprint = {2609.08565},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.08565},
}
RIS
TY  - UNPB
TI  - On the a-number of Fermat type function fields and some of their subfields
AU  - Marie Frank vom Braucke
PY  - 2026
DA  - 2026/09/08
PB  - arXiv
DO  - 10.48550/arxiv.2609.08565
UR  - https://arxiv.org/abs/2609.08565
AB  - The a-number of a function field F is the dimension of the kernel of the Cartier operator acting on the holomorphic differentials of F. We compute the action of the Cartier operator on the holomorphic differentials on the Hermitian function field ℋ, function fields of Fermat type ℱ_n,m and the Hurwitz function field ℋ_n. From this, we obtain various results about the a-number of these function fields, including a generalisation of the results on the Fermat function field from Kodama and Washio.
ER  -