论文标题
P-ADIC数字上的每7维阿贝尔品种都有一个还原
Every 7-Dimensional Abelian Variety over the p-adic Numbers has a Reducible $\ell$-adic Galois Representation
论文作者
论文摘要
让$ k $成为一个完整的，具有有限的残留场和$ g_k $的完整，具有离散价值的字段，其绝对Galois组。本说明的主题是研究一组正整数$ d $，其中存在绝对不可约的$ \ ell $ - $ adic代表$ g_k $ dimension $ d $的$ g_k $，具有惯性上的理性痕迹。我们的主要结果是，当$ k $的残留特性为$> 3 $时，非S-phophie Germain Primes不在此组中。标题中指出的结果是一个特殊情况。
Let $K$ be a complete, discretely valued field with finite residue field and $G_K$ its absolute Galois group. The subject of this note is the study of the set of positive integers $d$ for which there exists an absolutely irreducible $\ell$-adic representation of $G_K$ of dimension $d$ with rational traces on inertia. Our main result is that non-Sophie Germain primes are not in this set when the residue characteristic of $K$ is $> 3$. The result stated in the title is a special case.
