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arXiv · 1908.03321

Faltings Serre method on three dimensional selfdual representations

Lian Duan
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Abstract

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.

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Lian Duan. 2019-08-09. Faltings Serre method on three dimensional selfdual representations. https://doi.org/10.1090/mcom/3591

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