相容系统的辛伽罗瓦表示和逆伽罗瓦问题II。横截与巨像
Compatible systems of symplectic Galois representations and the inverse Galois problem II. Transvections and huge image
摘要：
这篇文章是一系列的三篇文章的第二部分关于兼容系统的辛伽罗瓦表示和应用的逆伽罗瓦问题。这一部分讨论了具有巨大余象的辛伽罗瓦表示，我们的意思是，在素域上的全维辛群包含到共轭。一个关键的成分是辛表示的分类，其图像包含一个非平凡的transvection：这些分为三个非常简单的描述类，可约的，诱导的和那些巨大的图像。利用Khare，Larsen和Savin的（n，p）-群的思想，我们给出了系数在有限域上的辛伽罗瓦表示具有巨象的简单条件.最后，我们把这个分类结果与第一部分的主要结果结合起来，得到了它在Galois逆问题中的一个加强应用。
英文摘要：
This article is the second part of a series of three articles about compatible systems of symplectic Galois representations and applications to the inverse Galois problem. This part is concerned with symplectic Galois representations having a huge residual image, by which we mean that a symplectic group of full dimension over the prime field is contained up to conjugation. A key ingredient is a classification of symplectic representations whose image contains a nontrivial transvection: these fall into three very simply describable classes, the reducible ones, the induced ones and those with huge image. Using the idea of an (n,p)-group of Khare, Larsen and Savin we give simple conditions under which a symplectic Galois representation with coefficients in a finite field has a huge image. Finally, we combine this classification result with the main result of the first part to obtain a strenghtened application to the inverse Galois problem.
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