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Local and global canonical height functions for affine space regular automorphisms
[article]
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
arXiv:0909.3573v1
fatcat:yg26wlujefarnb6m3douax7ud4