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

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

2008-04-15

arxiv.org/abs/0804.2302v2

Mathematics

Number Theory

21 pages

Scientific paper

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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