Equidistribution of dynamically small subvarieties over the function field of a curve
Equidistribution of dynamically small subvarieties over the function field of a curve
复制标题
动态小子品种在曲线函数域上的均匀分布
DOI：
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发表时间：
2008
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通讯作者：
X. Faber
中科院分区：
文献类型：
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作者：
X. Faber
对于定义在域K上的投射簇X，存在X的一类特殊的自态，称为代数动力系统。本文设K为光滑曲线的函数域，证明了在K的每一处，X的动态小高度的子簇在相应的Berkovich解析空间上均等分布.我们仔细开发所有的算术交叉理论需要国家和证明这一定理，我们提出了几个应用程序的非Zagliki密度的preperiodic点和点的小高度领域的扩展有界度。
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.