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Difference fields and descent in algebraic dynamics. II

Part of: Model theory Differential and difference algebra

Published online by Cambridge University Press:  07 October 2008

Zoé Chatzidakis  and
Ehud Hrushovski
Zoé Chatzidakis
Affiliation:
UFR de Mathématiques, Université Paris 7—Case 7012, Site Chevaleret, 75205 Paris Cedex 13, France (zoe@logique.jussieu.fr)
Ehud Hrushovski
Affiliation:
Institute of Mathematics, The Hebrew University, Givat Ram, 91904 Jerusalem, Israel (ehud@math.huji.ac.il) and Mathematics Department, Yale University, PO Box 208283, New Haven, CT 06520-8283, USA
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Abstract

This second part of the paper strengthens the descent theory described in the first part to rational maps and arbitrary base fields. We obtain in particular a decomposition of any difference field extension into a tower of finite, field-internal and one-based difference field extensions. This is needed in order to obtain the ‘dynamical Northcott’ Theorem 1.11 of Part I in sharp form.

Keywords

model theorydifference fieldsalgebraic dynamics

MSC classification

Secondary: 03C60: Model-theoretic algebra 12H10: Difference algebra
Type
Research Article
Information
Journal of the Institute of Mathematics of Jussieu , Volume 7 , Issue 4 , October 2008 , pp. 687 - 704
Copyright
Copyright © Cambridge University Press 2008

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