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Twisted Artin-Schreier Theory I: (Cp rtimes Cp−1)-extensions of local function fields

  • Béranger Seguin
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Abstract

Over any field K of characteristic p, we parametrize the (Cprtimes Cp−1)-extensions of K using pairs of elements (g,a) ∈ K× K×, via a "twisted" variant of Artin-Schreier theory. Focusing on the case of the local function field K := 𝔽q( (π) ) over a finite field 𝔽q of characteristic p, we use this parametrization to obtain an exact formula for the count of all (Cprtimes Cp−1)-extensions of K with a given discriminant.

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Cite

BibTeXRIS
BibTeX
@misc{seguin2026twisted,
  title = {{Twisted Artin-Schreier Theory I: $(C_p \rtimes C_p-1)$-extensions of local function fields}},
  author = {Béranger Seguin},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.21871},
  eprint = {2610.21871},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.21871},
}
RIS
TY  - UNPB
TI  - Twisted Artin-Schreier Theory I: (C_p rtimes C_p−1)-extensions of local function fields
AU  - Béranger Seguin
PY  - 2026
DA  - 2026/10/15
PB  - arXiv
DO  - 10.48550/arxiv.2610.21871
UR  - https://arxiv.org/abs/2610.21871
AB  - Over any field K of characteristic p, we parametrize the (C_prtimes C_p−1)-extensions of K using pairs of elements (g,a) ∈ K× K^×, via a "twisted" variant of Artin-Schreier theory. Focusing on the case of the local function field K := 𝔽_q( (π) ) over a finite field 𝔽_q of characteristic p, we use this parametrization to obtain an exact formula for the count of all (C_prtimes C_p−1)-extensions of K with a given discriminant.
ER  -