On modular forms and the inverse Galois problem
On modular forms and the inverse Galois problem
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关于模形式和逆伽罗瓦问题
DOI：
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发表时间：
2009
期刊：
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通讯作者：
G. Wiese
中科院分区：
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作者：
Luis Dieulefait;G. Wiese
本文建立了Galois逆问题的新的情形。主要结果是：对于一个固定的整数n，存在一个正的素数p的密度集，使得PSL 2（Fpn）作为有理数的某个有限扩张的Galois群出现.这些群体作为投影图像的剩余模块伽罗瓦表示。此外，族的模形式的构造，使其所有的剩余伽罗瓦表示的图像是尽可能大的先验可能。这两个结果本质上都是利用了Khare和Wintenberger的好二面体素数的概念。特别注意的是，以排除非平凡的内部扭曲。2000年数学学科分类：11 F80（小学）; 12 F12，11 F11。
In this article new cases of the Inverse Galois Problem are established. The main result is that for a fixed integer n, there is a positive density set of primes p such that PSL2(Fpn) occurs as the Galois group of some finite extension of the rational nu mbers. These groups are obtained as projective images of residual modular Galois representations. Moreover, families of modular forms are constructed such that the images of all their resid ual Galois representations are as large as a priori possible. Both results essentially use Khare’s a nd Wintenberger’s notion of gooddihedral primes. Particular care is taken in order to exclud e nontrivial inner twists. 2000 Mathematics Subject Classification: 11F80 (primary); 12F12, 11F11.