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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, we can associate to an automorphic representation a family of compatible l-adic representations. Our algorithm is based on Faltings-Serre's method to prove that l-adic Galois representations are isomorphic. Using the algorithm we provide the first examples of modular elliptic curves over imaginary quadratic fields with residual 2-adic image isomorphic to S3 and C3. © 2009 American Mathematical Society.

Registro:

Documento: Artículo
Título:Proving modularity for a given elliptic curve over an imaginary quadratic field
Autor:Dieulefait, L.; Guerberoff, L.; Pacetti, A.
Filiación:Departament d'Àlgebra i Geometria, Facultat de Matemàtiques, Universitat de Barcelona, Gran Via de les Corts Catalanes, 585, 08007 Barcelona, Spain
Departamento de Matemática, Universidad de Buenos Aires, Pabellón I, Ciudad Universitaria, C.P:1428, Buenos Aires, Argentina
Institut de Mathématiques de Jussieu, Université Paris 7, Denis Diderot, 2, place Jussieu, F-75251 Paris Cedex 05, France
Palabras clave:Elliptic curves modularity
Año:2010
Volumen:79
Número:270
Página de inicio:1145
Página de fin:1170
DOI: http://dx.doi.org/10.1090/S0025-5718-09-02291-1
Título revista:Mathematics of Computation
Título revista abreviado:Math. Comput.
ISSN:00255718
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00255718_v79_n270_p1145_Dieulefait

Referencias:

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Citas:

---------- APA ----------
Dieulefait, L., Guerberoff, L. & Pacetti, A. (2010) . Proving modularity for a given elliptic curve over an imaginary quadratic field. Mathematics of Computation, 79(270), 1145-1170.
http://dx.doi.org/10.1090/S0025-5718-09-02291-1
---------- CHICAGO ----------
Dieulefait, L., Guerberoff, L., Pacetti, A. "Proving modularity for a given elliptic curve over an imaginary quadratic field" . Mathematics of Computation 79, no. 270 (2010) : 1145-1170.
http://dx.doi.org/10.1090/S0025-5718-09-02291-1
---------- MLA ----------
Dieulefait, L., Guerberoff, L., Pacetti, A. "Proving modularity for a given elliptic curve over an imaginary quadratic field" . Mathematics of Computation, vol. 79, no. 270, 2010, pp. 1145-1170.
http://dx.doi.org/10.1090/S0025-5718-09-02291-1
---------- VANCOUVER ----------
Dieulefait, L., Guerberoff, L., Pacetti, A. Proving modularity for a given elliptic curve over an imaginary quadratic field. Math. Comput. 2010;79(270):1145-1170.
http://dx.doi.org/10.1090/S0025-5718-09-02291-1