On the arithmetic of abelian varieties
On the arithmetic of abelian varieties
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DOI：
10.1007/bf01425446
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发表时间：
1972-09
影响因子：
3.1
通讯作者：
J. Milne
中科院分区：
文献类型：
--
作者：
J. Milne
在w1中，我们考虑这样的情况：L/K是有限可分域扩展，a是L上的阿贝尔变分，a是由标量限制由a得到的K上的阿贝尔变分。我们研究了A相对于A的算术性质，并特别证明了Birch和Swinnerton-Dyer的猜想当且仅当它们对A成立时对A成立。
In w 1 we consider the situation: L/K is a finite separable field extension, A is an abelian variety over L, and A, is the abelian variety over K obtained from A by restriction of scalars. We study the arithmetic properties of A, relative to those of A, and in particular show that the conjectures of Birch and Swinnerton-Dyer hold for A if and only if they hold for A,.