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arXiv · 2504.13606

On the Hasse-Arf property of local fields

Ioannis Tsouknidas
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Abstract

Let $F/K$ be a finite Galois totally & wildly ramified extension of complete discrete valuation fields. We say that the extension has the Hasse-Arf property if the ramification jumps in upper numbering are integers. We give necessary defining equations for $F$ in terms of the ramification jumps. In order for the Hasse-Arf property to hold, these equations become very strict. We prove that the last assertion is an equivalence condition, thus in terms of these defining equations, the Hasse-Arf property becomes an equivalence condition.

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Ioannis Tsouknidas. 2025-04-18. On the Hasse-Arf property of local fields. https://arxiv.org/abs/2504.13606

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