发表机构
Universidade de São Paulo（圣保罗大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文研究赋值域纯扩张的分歧不变量，证明直接单分支情形下扩展迹理想由最小多项式导数生成，戴德金差为其除子闭包，并将结果推广到高次纯扩张及伽罗瓦情形。
AI 中文摘要
我们研究了在原始元素上为纯的赋值域有限可分扩张的分歧不变量。在直接单分支情形下，我们证明了扩展迹理想由整原始元素的最小多项式导数生成，且戴德金差是其除子闭包。对于伽罗瓦扩张，我们将该导数理想表示为子群分歧理想的乘积。这些公式将素数次计算推广到更高次的纯扩张。我们计算了一个次数为$p^2$的纯直接初等阿贝尔扩张的微分模、迹、差、分歧理想和特征斯旺理想。一个同次数的完全分歧例子给出了与无缺陷情形的比较。
英文摘要
We study ramification invariants of finite separable extensions of valued fields that are pure on a primitive element. In the immediate unibranched case, we prove that the extended trace ideal is generated by minimal-polynomial derivatives of integral primitive elements and that the Dedekind different is its divisorial closure. For Galois extensions, we express this derivative ideal as a product of subgroup ramification ideals. These formulas extend prime-degree calculations to pure extensions of higher degree. We compute the differential module, traces, differents, ramification ideals, and character Swan ideals of a pure immediate elementary abelian extension of degree $p^2$. A totally ramified example of the same degree gives a comparison with the defectless case.
