Faltings-Serre method on three dimensional selfdual representations
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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.References
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Additional Information
- Lian Duan
- Affiliation: Department of Mathematics, Colorado State University, Fort Collins, Colorado 80523
- ORCID: 0000-0003-4922-7831
- Email: lian.duan@colostate.edu
- Received by editor(s): October 9, 2019
- Received by editor(s) in revised form: July 29, 2020, and August 11, 2020
- Published electronically: November 3, 2020
- © Copyright 2020 American Mathematical Society
- Journal: Math. Comp. 90 (2021), 931-951
- MSC (2020): Primary 11Y40, 11F80
- DOI: https://doi.org/10.1090/mcom/3591
- MathSciNet review: 4194168