Dimension Polynomials of Intermediate Fields of Inversive Difference Field Extensions

  • Alexander LevinEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9582)


Let K be an inversive difference field, L a finitely generated inversive difference field extension of K, and F an intermediate inversive difference field of this extension. We prove the existence and establish properties and invariants of a numerical polynomial that describes the filtration of F induced by the natural filtration of the extension L/K associated with its generators. Then we introduce concepts of type and dimension of the extension L/K considering chains of its intermediate fields. Using properties of dimension polynomials of intermediate fields we obtain relationships between the type and dimension of L/K and difference birational invariants of this extension carried by its dimension polynomials. Finally, we present a generalization of the obtained results to the case of multivariate dimension polynomials associated with a given inversive difference field extension and a partition of the basic set of translations.


Inversive difference field Inversive difference module Filtration Dimension polynomial 


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© Springer International Publishing Switzerland 2016

Authors and Affiliations

  1. 1.The Catholic University of AmericaWashington, DCUSA

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