Equidistribution of dynamically small subvarieties over the function field of a curve
Abstract
For a projective variety X defined over a field K, there is a special class of selfmorphisms of X called algebraic dynamical systems. In this paper we take K to be the function field of a smooth curve and prove that at each place of K, subvarieties of X of dynamically small height are equidistributed on the associated Berkovich analytic space. We carefully develop all of the arithmetic intersection theory needed to state and prove this theorem, and we present several applications on the nonZariski density of preperiodic points and of points of small height in field extensions of bounded degree.
 Publication:

Acta Arithmetica
 Pub Date:
 2009
 DOI:
 10.4064/aa13744
 arXiv:
 arXiv:0801.4811
 Bibcode:
 2009AcAri.137..345F
 Keywords:

 Mathematics  Number Theory;
 Mathematics  Dynamical Systems;
 14G40;
 11G35
 EPrint:
 v2: Various typos fixed