论文标题
在$ \ mathbb {q} $的某些无限的Abelian扩展上，椭圆曲线的扭转组
Torsion groups of elliptic curves over some infinite abelian extensions of $\mathbb{Q}$
论文作者
论文摘要
我们确定，对于椭圆曲线$ e/\ mathbb {q} $，所有可能的扭转组$ e（k）_ {tors} $，其中$ k $是所有$ \ mathbb {z} _ {p} _ {p} $ - $ \ mathbb的扩展。此外，我们证明，对于椭圆曲线$ e/\ mathbb {q} $，它认为$ e（\ mathbb {q}（μ__{p^{\ infty}}}））_ {tors}）_ {tors} = e（ \ geq 5 $和$ e（\ mathbb {q}（μ_{3^{\ infty}}）））_ {tors} = e（\ mathbb {q}（μ__{3^3}））_ {tors}） $ e（\ mathbb {q}（μ_{2^{\ infty}}））_ {tors} = e（\ mathbb {q}（μ__{2^4}））_ {tors} $。
We determine, for an elliptic curve $E/\mathbb{Q}$, all the possible torsion groups $E(K)_{tors}$, where $K$ is the compositum of all $\mathbb{Z}_{p}$-extensions of $\mathbb{Q}$. Furthermore, we prove that for an elliptic curve $E/\mathbb{Q}$ it holds that $E(\mathbb{Q}(μ_{p^{\infty}}))_{tors} = E(\mathbb{Q}(μ_{p}))_{tors}$, for all primes $p \geq 5$ and $E(\mathbb{Q}(μ_{3^{\infty}}))_{tors} = E(\mathbb{Q}(μ_{3^3}))_{tors}$, $E(\mathbb{Q}(μ_{2^{\infty}}))_{tors} = E(\mathbb{Q}(μ_{2^4}))_{tors}$.
