The nonexistence of certain level structures on abelian varieties over complex function fields
The nonexistence of certain level structures on abelian varieties over complex function fields
复制标题
复函数域上阿贝尔簇上某些层次结构的不存在
DOI：
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发表时间：
1989
期刊：
影响因子：
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通讯作者：
A. Nadel
中科院分区：
文献类型：
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作者：
A. Nadel
设A是数域k上维数为g的主极化阿贝尔簇. Mordell-Weil定理告诉我们，A的k-有理点的群A（k）是n阶生成的;特别地，A（k）的挠子群是有限的。对于椭圆曲线E/Q的一个重要特例，Mazur [Mal，2]证明了E（Q）的挠子群的阶< 16.一般情况下，人们会期望A（k）的挠子群的阶< C（g，k），这是一个常数，只取决于数域k和维数g，但不依赖于
Let A be a principally polarized abelian variety of dimension g over a number field k. The Mordell-Weil theorem tells us that the group A(k) of k-rational points of A is finitely generated; in particular, the torsion subgroup of A(k) is finite. For the important special case of an elliptic curve E/Q, Mazur [Mal,2] has proved that the torsion subgroup of E(Q) has order < 16. In general one would expect the torsion subgroup of A(k) to have order < C(g, k), a constant depending only on the number field k and the dimension g but not