The module of Kähler differentials for extensions of valuation rings

2023/07/05 by Novacoski, Josnei, Spivakovsky, Mark
#Commutative Algebra (math.AC) #FOS: Mathematics

paper · doi:10.48550/arxiv.2307.02315

Abstract

The main goal of this paper is to characterize the module of Kähler differentials for an extension of valuation rings. More precisely, we consider a simple algebraic valued field extension (L/K,v) and the corresponding valuation rings \VR_L and \VR_K. In the case when e(L/K,v)=1 we present a characterization for Ω_\VRL/\VRK in terms of a given sequence of key polynomials for the extension. Moreover, we use our main result to present a characterization for when Ω_\VRL/\VRK=\0\.

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