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arXiv · 2610.21871

Twisted Artin-Schreier Theory I: $(C_p \rtimes C_{p-1})$-extensions of local function fields

Béranger Seguin
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Abstract

Over any field $K$ of characteristic $p$, we parametrize the $(C_p\rtimes C_{p-1})$-extensions of $K$ using pairs of elements $(g,a) \in K\times K^\times$, via a "twisted" variant of Artin-Schreier theory. Focusing on the case of the local function field $K := \mathbb F_q(\!(π)\!)$ over a finite field $\mathbb F_q$ of characteristic $p$, we use this parametrization to obtain an exact formula for the count of all $(C_p\rtimes C_{p-1})$-extensions of $K$ with a given discriminant.

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BibTeXRIS

Béranger Seguin. 2026-10-15. Twisted Artin-Schreier Theory I: $(C_p \rtimes C_{p-1})$-extensions of local function fields. https://arxiv.org/abs/2610.21871

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