论文标题
与桦木和Swinnerton-Dyer猜想有关的分裂性
A divisibility related to the Birch and Swinnerton-Dyer conjecture
论文作者
论文摘要
令$ e/\ mathbb {q} $为分析等级零的最佳椭圆曲线。它从桦木和swinnerton-dyer的猜想中，对于分析等级的椭圆曲线零，$ e/\ mathbb {q} $的扭力子组的顺序划分了$ e/\ mathbb {q} $ e/q $ e/b $ e/q n q $ e/q y shafarevich-tate of shafarevich-tate of shafarevich-tate的乘积。 Infinity的$ e/\ mathbb {q} $的tamagawa编号。 Agashe and Stein在2005年注意到了Birch和Swinnerton-Dyer猜想的这种后果。在本文中，我们在许多情况下无条件地证明了该划界性声明，包括曲线$ e/\ e/\ mathbb {q} $是半稳定的。
Let $E/\mathbb{Q}$ be an optimal elliptic curve of analytic rank zero. It follows from the Birch and Swinnerton-Dyer conjecture for elliptic curves of analytic rank zero that the order of the torsion subgroup of $E/\mathbb{Q}$ divides the product of the order of the Shafarevich--Tate group of $E/\mathbb{Q}$, the (global) Tamagawa number of $E/\mathbb{Q}$, and the Tamagawa number of $E/\mathbb{Q}$ at infinity. This consequence of the Birch and Swinnerton-Dyer conjecture was noticed by Agashe and Stein in 2005. In this paper, we prove this divisibility statement unconditionally in many cases, including the case where the curve $E/\mathbb{Q}$ is semi-stable.
