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arXiv · 0804.2302

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

Luis Dieulefait·Lucio Guerberoff·Ariel Pacetti
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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.

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Luis Dieulefait, Lucio Guerberoff, Ariel Pacetti. 2008-11-05. Proving modularity for a given elliptic curve over an imaginary quadratic field. https://arxiv.org/abs/0804.2302

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