# Local and global canonical height functions for affine space regular automorphisms

@article{Kawaguchi2009LocalAG,
title={Local and global canonical height functions for affine space regular automorphisms},
author={Shu Kawaguchi},
journal={arXiv: Algebraic Geometry},
year={2009}
}
• Shu Kawaguchi
• Published 19 September 2009
• Mathematics
• arXiv: Algebraic Geometry
Let f: A^N \to A^N be a regular polynomial automorphism defined over a number field K. For each place v of K, we construct the v-adic Green functions G_{f,v} and G_{f^{-1},v} (i.e., the v-adic canonical height functions) for f and f^{-1}. 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 the Northcott-type finiteness property. Using previous…

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