论文标题
潜在等效的GALOIS表示的有限定理：Faltings有限标准的扩展
Finiteness theorems for potentially equivalent Galois representations: extension of Faltings' finiteness criteria
论文作者
论文摘要
我们研究潜在的等效性与性格理论之间的关系。我们观察到，代表$ρ$的潜在等效性取决于某些自然数量$ m $的$ m $ power字符$ g \ mapsto tr（ρ（g^m））$。使用此过程，我们将Faltings的有限标准扩展到了一个数字字段的绝对Galois组的两个$ \ ell $ - adic，半度性表示的等效性，以归功于潜在等价性的上下文。 我们还讨论了扭曲未受到表示的有限结果。
We study the relationship between potential equivalence and character theory; we observe that potential equivalence of a representation $ρ$ is determined by an equality of an $m$-power character $g\mapsto Tr(ρ(g^m))$ for some natural number $m$. Using this, we extend Faltings' finiteness criteria to determine the equivalence of two $\ell$-adic, semisimple representations of the absolute Galois group of a number field, to the context of potential equivalence. We also discuss finiteness results for twist unramified representations.
