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Proving modularity for a given elliptic curve over an imaginary quadratic field

Dieulefait, L; Guerberoff, L; Pacetti, A; (2010) Proving modularity for a given elliptic curve over an imaginary quadratic field. Math. Comp. , 79 pp. 1145-1170. 10.1090/S0025-5718-09-02291-1. Green open access

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Abstract

We present an algorithm to determine if the $L$-series associated to an automorphic representation and the one associated to an elliptic curve over an imaginary quadratic field agree. By the work of Harris-Soudry-Taylor, Taylor and Berger-Harcos (cf. \cite{harris-taylor}, \cite{taylorII} and \cite{berger-harcos}) we can associate to an automorphic representation a family of compatible $p$-adic representations. Our algorithm is based on Faltings-Serre's method to prove that $p$-adic Galois representations are isomorphic.

Type: Article
Title: Proving modularity for a given elliptic curve over an imaginary quadratic field
Open access status: An open access version is available from UCL Discovery
DOI: 10.1090/S0025-5718-09-02291-1
Publisher version: https://doi.org/10.1090/S0025-5718-09-02291-1
Language: English
Additional information: This version is the author accepted manuscript. For information on re-use, please refer to the publisher’s terms and conditions.
Keywords: 11F80; 11G05
UCL classification: UCL
UCL > Provost and Vice Provost Offices
UCL > Provost and Vice Provost Offices > UCL BEAMS
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences
URI: https://discovery.ucl.ac.uk/id/eprint/1474963
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