Mathematische Annalen

, Volume 354, Issue 4, pp 1369–1396 | Cite as

A Chevalley theorem for difference equations

Article

Abstract

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.

Mathematics Subject Classification (2000)

12H10 39A05 

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Copyright information

© Springer-Verlag 2011

Authors and Affiliations

  1. 1.Lehrstuhl A für Mathematik, RWTH AachenAachenGermany

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