Deforming galois representations: Controlling the conductor
Deforming galois representations: Controlling the conductor
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变形伽罗瓦表示：控制导体
DOI：
10.1016/0022-314x(90)90055-v
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发表时间：
1990
期刊：
影响因子：
--
通讯作者：
F. Gouvêa
中科院分区：
文献类型：
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作者：
F. Gouvêa
这个问题与 Hida ([10],[11],[13],[121)、Mazur 和 Tilouine ([191)、Wiles ([25]) 以及作者 ((8},[9]) 最近的工作有关。本文第一部分介绍了 Mazur 基本设置的摘要。假设我们从一个与模块化形式（例如 N 级）相关的表示开始。然后询问 7J 的所有变形本身是否与模形式相关。为了有可能得到肯定的答案，我们必须询问变形是否附加到 N 级的 p 进模形式。这个问题在 [8] 中得到考虑，我们还指出了一个关键问题：在 Mazur 的理论中，我们考虑除 Np 之外的素数之外的所有变形；因此，它无法区分附加到 N 级和 N2 级的形式的表示，它们具有相同的素数。本文的目的是表明人们可以控制变形理论中的导体，从而控制模形式的水平。
This question relates to recent work of Hida ([10],[11],[13],[121), Mazur and Tilouine ([191), Wiles ([25]), and the author ((8},[9]). A summary of Mazur's basic set-up is presented in the first section of this paper. Suppose that we begin with a. representation which is associated to a modular form (of level N, say). Then it makes sense to ask whether all deformations of 7J are themselves associated to modular forms. For there to be any chance of a positive answer, we must ask whether the deformations are attached to p-adic modular forms of level N. This question is considered in [8], where we also point out a crucial problem: in Mazur's theory, one considers all deformations that are unramified outside the primes dividing Np; thus, it cannot distinguish representations attached to forms of level N and, say, N2, which have the same prime divisors. The point of this paper is to show that one can control the conductor in the deformation theory, and hence control the level of the modular forms