Dynamical canonical heights for Jordan blocks, arithmetic degrees of orbits, and nef canonical heights on abelian varieties
Dynamical canonical heights for Jordan blocks, arithmetic degrees of orbits, and nef canonical heights on abelian varieties
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Jordan 块的动态规范高度、算术轨道度数以及阿贝尔簇的 nef 规范高度
DOI：
10.1090/tran/6596
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发表时间：
2016
期刊：
影响因子：
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通讯作者：
Shu Kawaguchi and Joseph H. Silverman
中科院分区：
文献类型：
--
作者：
Shu Kawaguchi;Kazuhiko Yamaki;Shu Kawaguchi and Joseph H. Silverman
设在全局域上定义的正规射影变的自同态。证明了对于每一个，算术次的存在，是一个代数整数，并且在其上只取有限多个值。更进一步，如果是一个定义在数域上的阿贝尔变，是一个等基因，并且是一个轨道是Zariski密集的点，那么它等于的动力度。这些证明依赖于两个独立的结果。首先，构造一个具有on作用特征值的Jordan块，然后构造满足Jordan变换公式的正则高度函数。其次，如果是一个阿贝尔变体，并且正则高度与一个非零净除数相关联，则存在一个唯一的阿贝尔子变体，使得当且仅当。参考文献
Letbe an endomorphism of a normal projective variety defined over a global field. We prove that for every, the arithmetic degreeofexists, is an algebraic integer, and takes on only finitely many values asvaries over. Further, ifis an abelian variety defined over a number field,is an isogeny, andis a point whose-orbit is Zariski dense in, thenis equal to the dynamical degree of. The proofs rely on two results of independent interest. First, ifform a Jordan block with eigenvaluefor the action ofon, then we construct associated canonical height functionssatisfying Jordan transformation formulas. Second, ifis an abelian variety andis the canonical height onassociated to a nonzero nef divisor, then there is a unique abelian subvarietysuch thatif and only if. References