Kähler differentials, pure extensions and minimal key polynomials

2023/11/24 by Josnei Novacoski, Novacoski, Josnei, Mark Spivakovsky +1 · 1 citation
Mathematics · Physics and Astronomy · #Algebraic Geometry and Number Theory #Commutative Algebra (math.AC) #FOS: Mathematics #Geometry and complex manifolds #Nonlinear Waves and Solitons

paper · pdf · doi:10.48550/arxiv.2311.14322

openalex publication_date 2023/11/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The main object of study in this paper is the module Ω of Kähler differentials of an extension of valuation rings. We show that in the case of pure extensions Ω has a very good description. Namely, it is isomorphic to the quotient of two modules defined by final segments in the value group of the valuation. This allows us to describe the annihilator of Ω and to give criteria for Ω to be finitely generated and to be finitely presented. We also discuss how to relate the module of Kähler differentials of pure extensions to minimal key polynomials.

Citations

• On the computation of Kähler differentials and characterizations of Galois extensions with independent defect
• Minimal limit key polynomials

Cited by

• On the distances of an element to its conjugates

Related

• The module of Kähler differentials for extensions of valuation rings
• Kähler differentials of extensions of valuation rings and deeply ramified fields
• Key polynomials and minimal pairs
• On the computation of Kähler differentials and characterizations of Galois extensions with independent defect
• Generators for extensions of valuation rings