论文标题
高纤维化$ \ MATHCAL {S} _7 $ -CURVES PRIME导体
Hyperelliptic $\mathcal{S}_7$-curves of prime conductor
论文作者
论文摘要
如果$ {\ Mathbb Q} $上的$ {\ Mathbb Q} $，Abelian三倍$ a _ {/{\ mathbb q}} $，如果其2分区$ f $是$ {\ Mathcal s} _7 $ extension $ {\ Mathbb Q} $，而Ramifacience Index 7 $ {\ Mathbb Q} $，则是$ {\ MATHBB Q} 7 $ {\ MATHBB Q} ^ $ _________________________________________________________________________________2 $ {让$ a $有利，让$ b $是半固定的阿贝利安尺寸$ 3D $和导体$ n^d $，$ b [2] $由$ a [2] $过滤的$ b [2] $。我们在$ f $上提供了足够且可计算的课程理论标准，以确保$ b $对$ a^d $不相同。
An abelian threefold $A_{/{\mathbb Q}}$ of prime conductor $N$ is favorable if its 2-division field $F$ is an ${\mathcal S}_7$-extension over ${\mathbb Q}$ with ramification index 7 over ${\mathbb Q}_2$. Let $A$ be favorable and let $B$ be a semistable abelian variety of dimension $3d$ and conductor $N^d$ with $B[2]$ filtered by copies of $A[2]$. We give a sufficient and computable class field theoretic criterion on $F$ to guarantee that $B$ is isogenous to $A^d$.
