Open Access
2013 Local and global canonical height functions for affine space regular automorphisms
Shu Kawaguchi
Algebra Number Theory 7(5): 1225-1252 (2013). DOI: 10.2140/ant.2013.7.1225


Let f:ANAN be a regular polynomial automorphism defined over a number field K. For each place v of K, we construct the v-adic Green functions Gf,v and Gf1,v (i.e., the v-adic canonical height functions) for f and f1. Next we introduce for f the notion of good reduction at v, and using this notion, we show that the sum of v-adic Green functions over all v gives rise to a canonical height function for f that satisfies a Northcott-type finiteness property. Using an earlier result, we recover results on arithmetic properties of f-periodic points and non-f-periodic points. We also obtain an estimate of growth of heights under f and f1, which was independently obtained by Lee by a different method.


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Shu Kawaguchi. "Local and global canonical height functions for affine space regular automorphisms." Algebra Number Theory 7 (5) 1225 - 1252, 2013.


Received: 10 April 2012; Revised: 6 August 2012; Accepted: 4 September 2012; Published: 2013
First available in Project Euclid: 20 December 2017

zbMATH: 1302.37067
MathSciNet: MR3101078
Digital Object Identifier: 10.2140/ant.2013.7.1225

Primary: 37P30
Secondary: 11G50 , 37P05 , 37P20

Keywords: canonical height , local canonical height , regular polynomial automorphism

Rights: Copyright © 2013 Mathematical Sciences Publishers

Vol.7 • No. 5 • 2013
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