论文标题
对于某些椭圆形曲线，桦木和swinnerton-dyer的猜想具有复杂的乘法
The conjecture of Birch and Swinnerton-Dyer for certain elliptic curves with complex multiplication
论文作者
论文摘要
令$ e/f $为一个数字字段$ f $的椭圆曲线，并在想象中的二次字段$ k $中与整数复杂乘法。在假设$ l（e/f，1）\ neq 0 $和$ f（e_ {tors}）/k $是Abelian的假设下，我们提供了桦木和Swinnerton-dyer的猜想，以及其由Gross提出的象征性精炼的猜想。我们还证明了CM Abelian品种$ A/K $的结果。
Let $E/F$ be an elliptic curve over a number field $F$ with complex multiplication by the ring of integers in an imaginary quadratic field $K$. We give a complete proof of the conjecture of Birch and Swinnerton-Dyer for $E/F$, as well as its equivariant refinement formulated by Gross, under the assumption that $L(E/F,1)\neq 0$ and that $F(E_{tors})/K$ is abelian. We also prove analogous results for CM abelian varieties $A/K$.
