Local and global canonical height functions for affine space regular automorphisms [article]

Shu Kawaguchi
2009 arXiv   pre-print
Let f: A^N → 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 results, we
more » ... ecover 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 f^-1, which is independently obtained by Lee by a different method.
arXiv:0909.3573v1 fatcat:yg26wlujefarnb6m3douax7ud4