论文标题
关于高度Kummer-Faithful领域的注释
A note on highly Kummer-faithful fields
论文作者
论文摘要
我们介绍了一个高度的Kummer-Faithful领域的概念，并研究了其与Kummer-Faithful Fields概念的关系。我们还举例说明了高度kummer-Faithful领域的例子。例如，如果$ k $是$ \ mathbb {q} $的有限程度的数字字段，则$ g $是一个整数$> 0 $> 0 $和$ \ mathbf {m} =（m_p）_p $是一个非阴性整数的家族，是一个由$ p $ ranges cob ynextions $ g的$ k__________ \ g，mar与$ k $相邻的所有坐标$ p^{m_p} $ - 扭转子群$ a [p^{m_p}] $ $ a $的所有半阿伯利亚品种的$ a $ $ a $ a $ a $ a $ a $ a $ a $ k $ to $ k $在$ g $上，最多$ g $，所有质量数字$ p $ p $ p $ p $ p $，是高度kummer-firt的。
We introduce a notion of highly Kummer-faithful fields and study its relationship with the notion of Kummer-faithful fields. We also give some examples of highly Kummer-faithful fields. For example, if $k$ is a number field of finite degree over $\mathbb{Q}$, $g$ is an integer $>0$ and $\mathbf{m}=(m_p)_p$ is a family of non-negative integers, where $p$ ranges over all prime numbers, then the extension field $k_{g,\mathbf{m}}$ obtained by adjoining to $k$ all coordinates of the elements of the $p^{m_p}$-torsion subgroup $A[p^{m_p}]$ of $A$ for all semi-abelian varieties $A$ over $k$ of dimension at most $g$ and all prime numbers $p$, is highly Kummer-faithful.
