On the Bounded Height Conjecture
On the Bounded Height Conjecture
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关于有界高度猜想
DOI：
10.1093/imrn/rnn149
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发表时间：
2008
影响因子：
1
通讯作者：
P. Habegger
中科院分区：
文献类型：
--
作者：
P. Habegger
我们证明了 Bombieri、Masser 和 Zannier 提出的有界高度猜想：给定一个不可约闭子集 ，并用自然和 Zariski 开子集替换 X 后；余维所有代数子群的并集所包含的点的集合至少有界绝对Weil高度。如果子群的余维数至少为 ，我们将继续展示一些与 Zilber 和 Pink 的猜想相关的有限性结果。
We prove the Bounded Height Conjecture formulated by Bombieri, Masser, and Zannier: given an irreducible closed subvariety , and after replacing X by a natural and Zariski open subset; the set of its points contained in the union of all algebraic subgroups of codimension at least has bounded absolute Weil height. We proceed to show some finiteness results related to conjectures stated by Zilber and Pink, if the codimension of the subgroups is at least .