论文标题
绑定了主要两极分化的Abelian品种的图像导体，带有开放的Galois图像
A bound for the image conductor of a principally polarized abelian variety with open Galois image
论文作者
论文摘要
让$ a $是数字字段$ k $的主要两极分化的亚伯利亚尺寸$ g $。假设$ a $的Adelic Galois表示的图像是$ \ operatatorName {gsp} _ {2G}（\ hat {\ hat {\ Mathbb {z}}）$的开放子组。然后存在一个正整数$ m $，因此$ a $的Galois图像是其还原模型$ m $的完整预先映射。此属性的最低$ m $，表示为$ m_a $，称为$ a $的图像导体（也称为级别）。琼斯（Jones）最近就$ a $的标准不变式建立了$ m_a $的上限，就$ a $是椭圆曲线而没有复杂的乘法。在本文中，我们将上述结果概括为在任意维度中提供类似的结合。
Let $A$ be a principally polarized abelian variety of dimension $g$ over a number field $K$. Assume that the image of the adelic Galois representation of $A$ is an open subgroup of $\operatorname{GSp}_{2g}(\hat{\mathbb{Z}})$. Then there exists a positive integer $m$ so that the Galois image of $A$ is the full preimage of its reduction modulo $m$. The least $m$ with this property, denoted $m_A$, is called the image conductor (also called the level) of $A$. Jones recently established an upper bound for $m_A$, in terms of standard invariants of $A$, in the case that $A$ is an elliptic curve without complex multiplication. In this paper, we generalize the aforementioned result to provide an analogous bound in arbitrary dimension.
