Semi-stable Reduction Implies Minimality of the Resultant

For a dynamical system on n-dimensional projective space over a number field or a function field, we show that semi-stable reduction implies the minimality of the resultant. We use this to show that every such dynamical system over a number field admits a globally minimal presentation.

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Bibliographic Details
Main Authors Szpiro, Lucien, Tepper, Michael, Williams, Phillip
Format Journal Article
LanguageEnglish
Published 13.12.2012
Subjects
Mathematics - Algebraic Geometry
Mathematics - Dynamical Systems
Mathematics - Number Theory
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Summary:For a dynamical system on n-dimensional projective space over a number field or a function field, we show that semi-stable reduction implies the minimality of the resultant. We use this to show that every such dynamical system over a number field admits a globally minimal presentation.
DOI:10.48550/arxiv.1212.3391