Principally polarized ordinary abelian varieties over finite fields
Principally polarized ordinary abelian varieties over finite fields
复制标题
有限域上的主极化普通阿贝尔簇
DOI：
10.1090/s0002-9947-1995-1297531-4
复制
发表时间：
1995
期刊：
影响因子：
--
通讯作者：
Everett W. Howe
中科院分区：
文献类型：
--
作者：
Everett W. Howe
. Deligne证明了有限域A上的普通交换簇的范畴与具有附加结构的Z-模的范畴是等价的。我们翻译几个几何概念，包括极化，到德利涅的Z-模的类别。我们使用Deligne的等价性来刻画有限群方案在k上，作为核的极化的普通阿贝尔品种在一个给定的Isolation类在k上。我们的结果表明，有限域上的单奇维普通阿贝尔簇的每一个等距类都包含一个主极化簇。我们使用我们的结果，以完全刻画在有限域上，不包含主要极化品种的二维普通阿贝尔品种的Islam类的Weil数。最后，我们展示的几个issues类的绝对简单的四维普通阿贝尔品种在有限域，不包含主要极化品种的韦尔数。
. Deligne has shown that there is an equivalence from the category of ordinary abelian varieties over a finite field A: to a category of Z-modules with additional structure. We translate several geometric notions, including that of a polarization, into Deligne's category of Z-modules. We use Deligne's equivalence to characterize the finite group schemes over k that occur as kernels of polarizations of ordinary abelian varieties in a given isogeny class over k . Our result shows that every isogeny class of simple odd-dimensional ordinary abelian varieties over a finite field contains a principally polarized variety. We use our result to completely characterize the Weil numbers of the isogeny classes of two-dimensional ordinary abelian varieties over a finite field that do not contain principally polarized varieties. We end by exhibiting the Weil numbers of several isogeny classes of absolutely simple four-dimensional ordinary abelian varieties over a finite field that do not contain principally polarized varieties.