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Faltings-Serre method on three dimensional selfdual representations
Mathematics of Computation ( IF 2.2 ) Pub Date : 2020-11-03 , DOI: 10.1090/mcom/3591
Lian Duan

We prove that a selfdual $GL_3$-Galois representation constructed by van Geemen and Top is isomorphic to a quadratic twist of the symmetric square of the Tate module of an elliptic curve. This is an application of our refinement of the Faltings-Serre method to $3$-dimensional Galois representations with the ground field not equal to $\mathbb{Q}$. The proof makes use of the Faltings-Serre method, $\ell$-adic Lie algebra, and Burnside groups.

中文翻译:

三维自对偶表示的 Faltings-Serre 方法

我们证明了由 van Geemen 和 Top 构造的自对偶 $GL_3$-Galois 表示与椭圆曲线的 Tate 模的对称平方的二次扭曲同构。这是我们对 Faltings-Serre 方法的改进在 $3$ 维伽罗瓦表示中的应用,其中地面场不等于 $\mathbb{Q}$。证明使用了 Faltings-Serre 方法、$\ell$-adic 李代数和 Burnside 群。
更新日期:2020-11-03
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