Year: 2026
Type: preprint
Abstract: 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.
Source: arXiv (Cornell University)
Author: Novacoski, Josnei
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7220736039