Difference fields and descent in algebraic dynamics, II

2007/11/24 by Zoé Chatzidakis, Ehud Hrushovski, Chatzidakis, Zoé +1 · 5 citations
Computer Science · Mathematics · #03C60 #12H10 #14GXX #Advanced Differential Equations and Dynamical Systems #Advanced Topics in Algebra #Algebraic Geometry (math.AG) #FOS: Mathematics #Logic (math.LO) #Nonlinear Dynamics and Pattern Formation #math.AG #math.LO #msc:03C60 #msc:12H10 #msc:14GXX

paper · pdf · doi:10.48550/arxiv.0711.3865

Revised version; some corrections related to purely inseparable descent, with thanks to referee

openalex publication_date 2007/11/24 · arxiv created 2008/07/04 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

This second part of the paper strengthens the descent theory described in the first part to rational maps, arbitrary base fields, and dynamics given by correspondences. 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.

Cited by

• Model theory of difference fields with an additive character on the fixed field
• Dimension Polynomials for Affine Partial Difference Algebraic Groups
• A transformal transcendence result for algebraic difference equations
• When any four solutions are independent
• Automorphisms of valued fields: amalgamation and existential closedness

Related

• Difference fields and descent in algebraic dynamics - I
• A formulation of difference Galois theory
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• A transformal transcendence result for algebraic difference equations
• Descent for Algebraic Schemes