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arXiv · 2603.15544

Lifts of unramified twists and local-global principles

Fabian Gundlach·Béranger Seguin
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Abstract

We prove that two-step nilpotent $p$-extensions of rational global function fields of characteristic $p$ satisfy a quantitative local-global principle when they are counted according to their largest upper ramification break ("last jump"). We had previously shown this only for $p\neq2$. Compared to our previous proof, this proof is also more self-contained, and may apply to heights other than the last jump. As an application, we describe the distribution of last jumps of $D_4$-extensions of rational global function fields of characteristic $2$. We also exhibit a counterexample to the analogous local-global principle when counting by discriminants.

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Fabian Gundlach, Béranger Seguin. 2026-03-16. Lifts of unramified twists and local-global principles. https://arxiv.org/abs/2603.15544

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