论文标题
扭转场上阿贝尔品种的覆盖率分支
Ramified covers of abelian varieties over torsion fields
论文作者
论文摘要
我们研究了Abelian品种的分支封面上的某些无限galois扩展名的合理点。特别是，我们证明，每条椭圆曲线$ e $ a $ a $ aby $ \ mathbb {q} $在最大的Abelian Extension $ \ mathbb {q}^{Q}^{\ rm ab} $ $ \ m armbb {q imathbb {q} $ a的最大abelian extens $ \ mathbb {q}^{q} $ { tor}）$由毗邻到$ \ mathbb {q} $某些Abelian品种的所有扭转点$ a $ a $ a $ a $ a $ over $ \ mathbb {q} $。
We study rational points on ramified covers of abelian varieties over certain infinite Galois extensions of $\mathbb{Q}$. In particular, we prove that every elliptic curve $E$ over $\mathbb{Q}$ has the weak Hilbert property of Corvaja-Zannier both over the maximal abelian extension $\mathbb{Q}^{\rm ab}$ of $\mathbb{Q}$, and over the field $\mathbb{Q}(A_{\rm tor})$ obtained by adjoining to $\mathbb{Q}$ all torsion points of some abelian variety $A$ over $\mathbb{Q}$.
