论文标题
与全球功能字段有关的有效$ a $元素附加的Galois表示的一致性
Congruences of Galois representations attached to effective $A$-motives over global function fields
论文作者
论文摘要
本文调查了$ \ mathfrak {p} $的一致性 - 由有效的$ a $ a-motives产生的ADIC表示形式，该$ a $ - 摩托车在全球函数字段$ k $上定义。我们给出了两个一致的$ \ mathfrak {p} $的标准 - ADIC表示来自强烈的半稳定有效$ a $ a $ otives，当限于$ k $的合适位置的分解组时，最直至半简化。这是Ozeki-Taguchi标准的函数字段类似物，用于数字字段的$ \ ell $ adiC表示。由Rasmussen和Tamagawa陈述的Abelian品种对Abelian品种的不存在猜想的动机，我们还表明，没有具有某些约束的强大半稳定有效$ A $ a $ a $ a $ a。
This article investigates congruences of $\mathfrak{p}$-adic representations arising from effective $A$-motives defined over a global function field $K$. We give a criterion for two congruent $\mathfrak{p}$-adic representations coming from strongly semi-stable effective $A$-motives to be isomorphic up to semi-simplification when restricted to decomposition groups of suitable places of $K$. This is a function field analog of Ozeki-Taguchi's criterion for $\ell$-adic representations of number fields. Motivated by a non-existence conjecture on abelian varieties over number fields stated by Rasmussen and Tamagawa, we also show that there exist no strongly semi-stable effective $A$-motives with some constrained.
