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Abstract:

Let 2+54 denote the double cover of S4 corresponding to the element in H2(54, ℤ/2ℤ) where transpositions lift to elements of order 2 and the product of two disjoint transpositions to elements of order 4. Given an elliptic curve E, let E[2] denote its 2-torsion points. Under some conditions on E elements in H 1(Galℚ, E[2])\\{0} correspond to Galois extensions N of ℚ with Galois group (isomorphic to) 54. In this work we give an interpretation of the addition law on such fields, and prove that the obstruction for N having a Galois extension Ñ with Gal(Ñ/ℚ) ≃ 2+54 gives a homomorphism s4 +: H1(Galℚ, E[2]) → H 2(Galℚ, ℤ/2ℤ). As a corollary we can prove (if E has conductor divisible by few primes and high rank) the existence of 2-dimensional representations of the absolute Galois group of ℚ attached to E and use them in some examples to construct 3/2 modular forms mapping via the Shimura map to (the modular form of weight 2 attached to) E. © 2007 American Mathematical Society.

Registro:

Documento: Artículo
Título:On the embedding problem for 2+S4 representations
Autor:Pacetti, A.
Filiación:Departamento de Matemática, Universidad de Buenos Aires, Ciudad Universitaria, Pabellón I, C.P:1428, Buenos Aires, Argentina
Palabras clave:Galois representations; Shimura correspondence
Año:2007
Volumen:76
Número:260
Página de inicio:2063
Página de fin:2075
DOI: http://dx.doi.org/10.1090/S0025-5718-07-01940-0
Título revista:Mathematics of Computation
Título revista abreviado:Math. Comput.
ISSN:00255718
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00255718_v76_n260_p2063_Pacetti

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Citas:

---------- APA ----------
(2007) . On the embedding problem for 2+S4 representations. Mathematics of Computation, 76(260), 2063-2075.
http://dx.doi.org/10.1090/S0025-5718-07-01940-0
---------- CHICAGO ----------
Pacetti, A. "On the embedding problem for 2+S4 representations" . Mathematics of Computation 76, no. 260 (2007) : 2063-2075.
http://dx.doi.org/10.1090/S0025-5718-07-01940-0
---------- MLA ----------
Pacetti, A. "On the embedding problem for 2+S4 representations" . Mathematics of Computation, vol. 76, no. 260, 2007, pp. 2063-2075.
http://dx.doi.org/10.1090/S0025-5718-07-01940-0
---------- VANCOUVER ----------
Pacetti, A. On the embedding problem for 2+S4 representations. Math. Comput. 2007;76(260):2063-2075.
http://dx.doi.org/10.1090/S0025-5718-07-01940-0