Multivariate counting of wild abelian extensions

Fabian Gundlach

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arXiv · 2607.27364

Multivariate counting of wild abelian extensions

Fabian Gundlach

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Abstract

Let $K$ be a global function field of characteristic~$p$ and let $G$ be a finite abelian group of exponent $p^e$. We show that the multivariate generating function counting sub-$G$-extensions of $K$ with respect to $e$ specific height functions (encoding successive drops in the exponents of the higher ramification groups) is rational.

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Fabian Gundlach. 2026-07-29. Multivariate counting of wild abelian extensions. https://arxiv.org/abs/2607.27364

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