论文标题
相对于障碍物2
Serre curves relative to obstructions modulo 2
论文作者
论文摘要
我们考虑椭圆形曲线$ e / \ mathbb {q} $，为此，如果限制了对图像模拟2的限制，则在此曲线上尽可能大。对于此类曲线，我们给出了$ \ ell $ - aadic图像的特征，以$ 500,000的umpuctor $ \ ell $ - expore $描述$ $ supporte $，并在500,000 $上描述了$ s的应用。循环问题。通过这种方式，我们将一些基本结果推广到Serre曲线上。
We consider elliptic curves $E / \mathbb{Q}$ for which the image of the adelic Galois representation $ρ_E$ is as large as possible given a constraint on the image modulo 2. For such curves, we give a characterization in terms of their $\ell$-adic images, compute all examples of conductor at most 500,000, precisely describe the image of $ρ_E$, and offer an application to the cyclicity problem. In this way, we generalize some foundational results on Serre curves.
