On Serre's uniformity conjecture for semistable elliptic curves over totally real fields
On Serre's uniformity conjecture for semistable elliptic curves over totally real fields
复制标题
关于全实域上半稳定椭圆曲线的塞尔均匀性猜想
DOI：
10.1007/s00209-015-1478-8
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发表时间：
2015
影响因子：
0.8
通讯作者：
Anni S
中科院分区：
文献类型：
--
作者：
Anni S
设是一个全实数域，并设为的有限个非阿基米德位置集。根据Merel，Momose和David的工作，存在一个常数，使得如果定义了一条椭圆曲线，在外部是半稳定的，那么对所有人来说，表示是不可约的。我们将其与模性和水平降低相结合，以证明存在一个有效可计算的常量，以及一个有效可计算的椭圆曲线集，使得下列条件成立。如果椭圆曲线是外超半稳定的，并且是素数，那么要么是满射，要么是对某些满射。
Letbe a totally real field, and letbe a finite set of non-archimedean places of. It follows from the work of Merel, Momose and David that there is a constantso that ifis an elliptic curve defined over, semistable outside, then for all, the representationis irreducible. We combine this with modularity and level lowering to show the existence of an effectively computable constant, and an effectively computable set of elliptic curves overwith CMsuch that the following holds. Ifis an elliptic curve oversemistable outside, andis prime, then eitheris surjective, orfor some.