Equidistribution of Dynamically Small Subvarieties over the Function Field of a Curve

Details Equidistribution of Dynamically Small Subvarieties over the Function Field of a Curve Equidistribution of Dynamically Small Subvarieties over the Function Field of a Curve

2008-01-31

arxiv.org/abs/0801.4811v3

Mathematics

Number Theory

v2: Various typos fixed; statement and proof of auxiliary Prop. 6.1 corrected. During the process of preparing this manuscript

Scientific paper

For a projective variety X defined over a field K, there is a special class of self-morphisms 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 non-Zariski density of preperiodic points and of points of small height in field extensions of bounded degree.

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