论文标题
塔川数的椭圆形曲线与扭转点
Tamagawa numbers of elliptic curves with torsion points
论文作者
论文摘要
让$ k $为全球领域，让$ e/k $为椭圆形曲线，具有$ k $ - 理性订单$ p $。在本文中，我们对$ e/k $的（全球）tamagawa $ c（e/k）$ c（e/k）的频率很感兴趣，可除以$ p $。考虑到分数$ c（e/ k）/ | e（k）_ {\ text {tors}} | $出现在桦木和swinnerton-dyer猜想的第二部分中，这是一个自然的问题。我们专注于在全球字段上定义的椭圆曲线，但我们也证明了在$ \ Mathbb {q} $上定义的更高维的Abelian品种的结果。
Let $K$ be a global field and let $E/K$ be an elliptic curve with a $K$-rational point of prime order $p$. In this paper we are interested in how often the (global) Tamagawa number $c(E/K)$ of $E/K$ is divisible by $p$. This is a natural question to consider in view of the fact that the fraction $c(E/K)/ |E(K)_{\text{tors}}|$ appears in the second part of the Birch and Swinnerton-Dyer Conjecture. We focus on elliptic curves defined over global fields, but we also prove a result for higher dimensional abelian varieties defined over $\mathbb{Q}$.
