Automorphic Galois representations and the inverse Galois problem for certain groups of type 𝐷_{𝑚},Proceedings of the American Mathematical Society

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Automorphic Galois representations and the inverse Galois problem for certain groups of type 𝐷_{𝑚}
Proceedings of the American Mathematical Society ( IF 1 ) Pub Date : 2020-10-20 , DOI: 10.1090/proc/15253
Adrián Zenteno

Abstract:Let

be an integer greater than three and $\ell$ be an odd prime. In this paper we prove that at least one of the following groups: $\mathrm {P}\Omega ^\pm _{2m}(\mathbb{F}_{\ell ^s})$ , $\mathrm {PSO}^\pm _{2m}(\mathbb{F}_{\ell ^s})$ , $\mathrm {PO}_{2m}^\pm (\mathbb{F}_{\ell ^s})$ , or $\mathrm {PGO}^\pm _{2m}(\mathbb{F}_{\ell ^s})$ is a Galois group of $\mathbb{Q}$ for infinitely many integers

. This is achieved by making use of a slight modification of a group theory result of Khare, Larsen, and Savin, and previous results of the author on the images of the Galois representations attached to cuspidal automorphic representations of $\mathrm {GL}_{2m}(\mathbb{A}_\mathbb{Q})$ .

中文翻译：

morph_ {𝑚}类型某些群的自守伽罗瓦表示和伽罗瓦逆问题

摘要：让

整数大于3并 $\ ell$ 成为奇数质数。在本文中，我们证明了以下组的至少一个：，，，或者是伽罗瓦组为无限多的整数。这是通过对Khare，Larsen和Savin的群论结果以及作者先前在Galois表示的图像上附加到尖峰的自构形表示的图像进行的稍微修改而实现的。 $\ mathrm {P} \ Omega ^ \ pm _ {2m}（\ mathbb {F} _ {\ ell ^ s}）$ $\ mathrm {PSO} ^ \ pm _ {2m}（\ mathbb {F} _ {\ ell ^ s}）$ $\ mathrm {PO} _ {2m} ^ \ pm（\ mathbb {F} _ {\ ell ^ s}）$ $\ mathrm {PGO} ^ \ pm _ {2m}（\ mathbb {F} _ {\ ell ^ s}）$ $\ mathbb {Q}$

$\ mathrm {GL} _ {2m}（\ mathbb {A} _ \ mathbb {Q}）$

更新日期：2020-10-20

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