2010/10/25 by Michael Wibmer, Wibmer, Michael · 2 citations
Computer Science · Mathematics · #12H10 "Primary" #39A05 "Secondary" #Advanced Differential Equations and Dynamical Systems #Algebraic Geometry (math.AG) #Commutative Algebra (math.AC) #FOS: Mathematics #Polynomial and algebraic computation #Rings, Modules, and Algebras
paper · pdf · doi:10.48550/arxiv.1010.5066
openalex publication_date 2010/10/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
By a theorem of Chevalley the image of a morphism of varieties is a constructible set. The algebraic version of this fact is usually stated as a result on "extension of specializations" or "lifting of prime ideals". We present a difference analog of this theorem. The approach is based on the philosophy that occasionally one needs to pass to higher powers of σ, where σ is the endomorphism defining the difference structure. In other words, we consider difference pseudo fields (which are finite direct products of fields) rather than difference fields. We also prove a result on compatibility of pseudo fields and present some applications of the main theorem, e.g. constrained extension and uniqueness of differential Picard-Vessiot rings with a difference parameter.