Proving modularity for a given elliptic curve over an imaginary quadratic field
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 fa...
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| Formato: | JOUR |
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| Acceso en línea: | http://hdl.handle.net/20.500.12110/paper_00255718_v79_n270_p1145_Dieulefait |
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todo:paper_00255718_v79_n270_p1145_Dieulefait2023-10-03T14:36:12Z Proving modularity for a given elliptic curve over an imaginary quadratic field Dieulefait, L. Guerberoff, L. Pacetti, A. Elliptic curves modularity 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. JOUR info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar http://hdl.handle.net/20.500.12110/paper_00255718_v79_n270_p1145_Dieulefait |
| institution |
Universidad de Buenos Aires |
| institution_str |
I-28 |
| repository_str |
R-134 |
| collection |
Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) |
| topic |
Elliptic curves modularity |
| spellingShingle |
Elliptic curves modularity Dieulefait, L. Guerberoff, L. Pacetti, A. Proving modularity for a given elliptic curve over an imaginary quadratic field |
| topic_facet |
Elliptic curves modularity |
| description |
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. |
| format |
JOUR |
| author |
Dieulefait, L. Guerberoff, L. Pacetti, A. |
| author_facet |
Dieulefait, L. Guerberoff, L. Pacetti, A. |
| author_sort |
Dieulefait, L. |
| title |
Proving modularity for a given elliptic curve over an imaginary quadratic field |
| title_short |
Proving modularity for a given elliptic curve over an imaginary quadratic field |
| title_full |
Proving modularity for a given elliptic curve over an imaginary quadratic field |
| title_fullStr |
Proving modularity for a given elliptic curve over an imaginary quadratic field |
| title_full_unstemmed |
Proving modularity for a given elliptic curve over an imaginary quadratic field |
| title_sort |
proving modularity for a given elliptic curve over an imaginary quadratic field |
| url |
http://hdl.handle.net/20.500.12110/paper_00255718_v79_n270_p1145_Dieulefait |
| work_keys_str_mv |
AT dieulefaitl provingmodularityforagivenellipticcurveoveranimaginaryquadraticfield AT guerberoffl provingmodularityforagivenellipticcurveoveranimaginaryquadraticfield AT pacettia provingmodularityforagivenellipticcurveoveranimaginaryquadraticfield |
| _version_ |
1807318735153790976 |