Faltings-Serre method on three dimensional selfdual representations

Duan, Lian

doi:10.1090/mcom/3591

Faltings-Serre method on three dimensional selfdual representations
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Math. Comp. 90 (2021), 931-951 Request permission

Abstract:

We prove that a $3$-dimensional selfdual 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 $\ell$-adic selfdual representations with the ground field not equal to $\mathbf {Q}$. The proof makes use of the Faltings-Serre method and Burnside groups.

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