On the Existence of Absolutely Simple Abelian Varieties of a Given Dimension over an Arbitrary Field
On the Existence of Absolutely Simple Abelian Varieties of a Given Dimension over an Arbitrary Field
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论任意域上给定维度的绝对简单阿贝尔簇的存在性
DOI：
10.1006/jnth.2001.2697
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发表时间：
2000
影响因子：
0.7
通讯作者：
H. Zhu
中科院分区：
文献类型：
--
作者：
Everett W. Howe;H. Zhu
本文证明了对任意域k和任意正整数n，存在k上的n维绝对单阿贝尔簇。我们还证明了有限域的一个渐近结果：对于任意的有限域k和正整数n，设S（k，n）表示k上n维阿贝尔簇的等距类中由绝对单的普通阿贝尔簇组成的分数.则对于每一个n，我们有S（F q，n）→1，因为q →∞在素幂上。
Abstract We prove that for every field k and every positive integer n there exists an absolutely simple n -dimensional abelian variety over k . We also prove an asymptotic result for finite fields: For every finite field k and positive integer n , we let S ( k , n ) denote the fraction of the isogeny classes of n -dimensional abelian varieties over k that consist of absolutely simple ordinary abelian varieties. Then for every n we have S ( F q , n )→1 as q →∞ over the prime powers.