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
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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
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Palabras clave: | Elliptic curves modularity |
Año: | 2010
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Volumen: | 79
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Número: | 270
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Página de inicio: | 1145
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Página de fin: | 1170
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DOI: |
http://dx.doi.org/10.1090/S0025-5718-09-02291-1 |
Título revista: | Mathematics of Computation
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Título revista abreviado: | Math. Comput.
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ISSN: | 00255718
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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